Edit Profile (opens in new tab) Borisov, Denis Ivanovich Compute Distance To: Compute Author ID: borisov.denis-i Published as: Borisov, D. I.; Borisov, Denis; Borisov, Denis I.; Borisov, D.; Borisov, Denis Ivanovich more...less Homepage: http://borisovdi.narod.ru/ External Links: MGP · ORCID · Math-Net.Ru · dblp Documents Indexed: 121 Publications since 1999 Reviewing Activity: 45 Reviews Co-Authors: 39 Co-Authors with 78 Joint Publications 908 Co-Co-Authors all top 5 Co-Authors 39 single-authored 13 Cardone, Giuseppe 11 Veselić, Ivan 7 Freitas, Pedro 7 Gadyl’shin, Rustem R. 7 Znojil, Miloslav 6 Exner, Pavel 5 Konyrkulzhaeva, Maral Nurlanovna 5 Mukhametrakhimova, A. I. 5 Zezyulin, Dmitry A. 4 Bunoiu, Renata 4 Golovina, Anastasiya Mihajlovna 3 Dmitriev, Sergey V. 3 Krejčiřík, David 3 Pankrashkin, Konstantin 3 Tautenhahn, Martin 2 Durante, Tiziana 2 Hoecker-Escuti, Francisco 2 Kevrekidis, Panayotis G. 2 Saadatmand, Danial 2 Täufer, Matthias 1 Bikmetov, Aĭdar Renatovich 1 Chechkin, Gregory Aleksandrovich 1 Ekholm, Tomas 1 Faella, Luisa 1 Fatykhov, Minnekhan A. 1 Gaydukov, R. K. 1 Gazizova, L. I. 1 Golovina, Anastasia 1 Javidan, Kurosh 1 Koroleva, Yulia O. 1 Kovařík, Hynek 1 Nakić, Ivica 1 Perugia, Carmen 1 Piatnitski, Andrey L. 1 Rose, Christian 1 Ružička, František 1 Sharapov, Timur Farkhatovich 1 Sultanov, Oskar A. 1 Zhizhina, Elena Anatol’evna 1 Zhou, Kun all top 5 Serials 18 Journal of Mathematical Sciences (New York) 6 Journal of Mathematical Physics 6 Doklady Mathematics 5 Mathematical Notes 5 Theoretical and Mathematical Physics 5 Sbornik: Mathematics 5 Annales Henri Poincaré 4 Russian Journal of Mathematical Physics 4 Proceedings of the Steklov Institute of Mathematics 4 Journal of Physics A: Mathematical and Theoretical 3 Journal of Mathematical Analysis and Applications 3 Journal of Differential Equations 3 Journal of Functional Analysis 3 Izvestiya: Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Ufimskiĭ Matematicheskiĭ Zhurnal 2 Journal of Statistical Physics 2 Functional Analysis and its Applications 2 Studies in Applied Mathematics 2 Asymptotic Analysis 2 Annals of Physics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Communications in Nonlinear Science and Numerical Simulation 2 Communications in Contemporary Mathematics 1 International Journal of Theoretical Physics 1 Nuclear Physics. B 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Advances in Mathematics 1 Integral Equations and Operator Theory 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Problemy Matematicheskogo Analiza 1 Mathematical Physics, Analysis and Geometry 1 Visnyk Kharkivs’kogo Universytetu. Seriya Matematyka, Prykladna Matematyka i Mekhanika 1 Differential Equations 1 Analysis & PDE 1 Analysis and Mathematical Physics all top 5 Fields 83 Partial differential equations (35-XX) 39 Quantum theory (81-XX) 35 Operator theory (47-XX) 20 Ordinary differential equations (34-XX) 12 Statistical mechanics, structure of matter (82-XX) 5 Probability theory and stochastic processes (60-XX) 4 Optics, electromagnetic theory (78-XX) 3 Combinatorics (05-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Algebraic geometry (14-XX) 2 Approximations and expansions (41-XX) 2 Fluid mechanics (76-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 94 Publications have been cited 705 times in 299 Documents Cited by ▼ Year ▼ Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\). Zbl 1180.35397Borisov, Denis; Freitas, Pedro 29 2010 Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066Borisov, D. I. 29 2006 Bound states in weakly deformed strips and layers. Zbl 1043.35046Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D. 27 2001 Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 27 2016 Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094Borisov, D.; Exner, P.; Gadyl’shin, R. 26 2002 Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401Borisov, Denis; Freitas, Pedro 26 2009 Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088Borisov, D.; Cardone, G. 26 2009 Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 23 2013 \(\mathcal {PT}\)-symmetric waveguides. Zbl 1178.35141Borisov, Denis; Krejčiřík, David 22 2008 On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 22 2010 Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen 21 2013 Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008Borisov, D.; Exner, P. 20 2004 Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050Borisov, Denis; Pankrashkin, Konstantin 18 2013 On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308Borisov, Denis I. 16 2003 On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056Borisov, D. I.; Gadyl’shin, R. R. 16 2008 Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046Borisov, D. I.; Pankrashkin, K. V. 15 2013 Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075Borisov, Denis I. 14 2007 Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155Borisov, Denis 14 2007 Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038Borisov, D.; Bunoiu, R.; Cardone, G. 12 2011 Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151Borisov, Denis; Freitas, Pedro 12 2009 Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek 11 2005 Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029Borisov, D. 11 2009 Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043Borisov, D.; Exner, P. 10 2006 Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100Borisov, Denis; Cardone, Giuseppe 9 2011 On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066Borisov, D. I. 9 2011 Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248Borisov, Denis; Cardone, Giuseppe 9 2011 The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042Borisov, Denis; Krejčiřík, David 9 2012 Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051Borisov, Denis; Veselić, Ivan 9 2013 On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 9 2011 The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023Borisov, D. I.; Mukhametrakhimova, A. I. 8 2018 Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055Borisov, D. I. 8 2003 The spectrum of two quantum layers coupled by a window. Zbl 1115.81024Borisov, D. 8 2007 Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089Borisov, Denis; Veselić, Ivan 8 2011 On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134Borisov, D. I. 7 2015 Some singular perturbations of periodic operators. Zbl 1147.34060Borisov, D. I. 7 2007 Tunneling resonances in systems without a classical trapping. Zbl 1280.81035Borisov, D.; Exner, P.; Golovina, A. 6 2013 Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108Borisov, Denis; Cardone, Giuseppe 6 2012 Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan 6 2017 The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107Borisov, D. I.; Gadyl’shin, R. R. 6 2006 Asymptotics for the expected lifetime of Brownian motion on thin domains in \(\mathbb R^n\). Zbl 1296.60220Borisov, Denis; Freitas, Pedro 5 2013 On the extrema of band functions in periodic waveguides. Zbl 1308.34111Borisov, D. I.; Pankrashkin, K. V. 5 2013 On eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin layer. Zbl 1371.35178Borisov, Denis I.; Znojil, Miloslav 5 2017 On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. Zbl 1321.47166Borisov, D. I. 5 2013 Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172Znojil, Miloslav; Borisov, Denis I. 5 2018 On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305Borisov, D. I.; Dmitriev, S. V. 5 2017 Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039Borisov, D. I.; Konyrkulzhaeva, M. N. 4 2019 Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047Borisov, D. I. 4 2002 Two-parameter asymptotics in a boundary value problem for the Laplacian. Zbl 1140.35544Borisov, D. I. 4 2001 Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037Borisov, Denis I.; Ružička, František; Znojil, Miloslav 4 2015 Kink scattering from a parity-time-symmetric defect in the \(\phi^4\) model. Zbl 07246123Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh 4 2015 Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118Borisov, D. I.; Gaydukov, R. K. 4 2016 The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039Borisov, D. I.; Gadyl’shin, R. R. 4 2007 On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054Borisov, D. I.; Sharapov, T. F. 4 2016 On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059Borisov, D. I.; Mukhametrakhimova, A. I. 4 2020 Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 3 2014 Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032Borisov, D. I. 3 2004 On the spectrum of the Laplacian with frequently alternating boundary conditions. Zbl 0945.35066Borisov, D. I.; Gadyl’shin, R. R. 3 1999 Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020Borisov, D. I. 3 2018 Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028Borisov, D. I.; Zezyulin, D. A. 3 2020 Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 3 2018 Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039Borisov, Denis; Golovina, Anastasia; Veselić, Ivan 3 2016 Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Zbl 1480.35140Borisov, D. I.; Mukhametrakhimova, A. I. 3 2021 On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261Borisov, Denis; Freitas, Pedro 2 2013 Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 2 2016 The spectrum of geodesic balls on spherically symmetric manifolds. Zbl 1380.53047Borisov, Denis; Freitas, Pedro 2 2017 Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169Borisov, D. I. 2 2019 Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient. Zbl 07263227Saadatmand, Danial; Borisov, Denis I.; Kevrekidis, Panayotis G.; Zhou, Kun; Dmitriev, Sergey V. 2 2018 Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna 2 2019 On a Laplacian with frequently nonperiodically alternating boundary conditions. Zbl 1197.35027Borisov, D. I. 2 2002 On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337Borisov, D. I. 2 2006 On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071Borisov, D. I. 2 2006 Norm resolvent convergence of elliptic operators in domains with thin spikes. Zbl 1486.35021Borisov, D. I. 2 2022 Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan 2 2015 Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037Borisov, D.; Tautenhahn, M.; Veselić, I. 2 2015 Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050Borisov, D. I.; Zezyulin, D. A.; Znojil, M. 2 2021 Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020Borisov, D.; Sultanov, O. 2 2020 Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062Borisov, D. I. 1 2019 Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058Borisov, D. I. 1 2019 On a singularly perturbed boundary value problem for the Laplacian in a cylinder. Zbl 1274.35013Borisov, D. I. 1 2002 Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162Borisov, D. I. 1 2015 Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan 1 2018 On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation. Zbl 1463.35386Borisov, Denis Ivanovich 1 2018 Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations. Zbl 1479.35582Borisov, D. I.; Zezyulin, D. A. 1 2021 Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144Bikmetov, A. R.; Borisov, D. I. 1 2005 Analytic continuation of resolvents of elliptic operators in a multidimensional cylinder. Zbl 07251966Borisov, D. I.; Golovina, A. M.; Mukhametrakhimova, A. I. 1 2020 The spectrum of a periodic operator with a small localized perturbation. Zbl 1175.34106Borisov, D. I.; Gadyl’shin, R. R. 1 2007 On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018Borisov, D. I.; Golovina, A. M. 1 2021 Quantum graphs with small edges: holomorphy of resolvents. Zbl 1479.81026Borisov, D. I. 1 2021 Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions. Zbl 1495.35017Borisov, D. I. 1 2022 Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143Borisov, D. I. 1 2016 On discrete spectrum of a model graph with loop and small edges. Zbl 1472.81069Borisov, D. I.; Konyrkulzhaeva, M. N.; Mukhametrakhimova, A. I. 1 2021 Anomalous mechanisms of the loss of observability in non-Hermitian quantum models. Zbl 1473.81151Znojil, Miloslav; Borisov, Denis I. 1 2020 Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. Zbl 1402.81149Borisov, Denis I.; Znojil, Miloslav 1 2016 Analyticity of resolvents of elliptic operators on quantum graphs with small edges. Zbl 1485.81032Borisov, D. I. 1 2022 Norm resolvent convergence of elliptic operators in domains with thin spikes. Zbl 1486.35021Borisov, D. I. 2 2022 Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions. Zbl 1495.35017Borisov, D. I. 1 2022 Analyticity of resolvents of elliptic operators on quantum graphs with small edges. Zbl 1485.81032Borisov, D. I. 1 2022 Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Zbl 1480.35140Borisov, D. I.; Mukhametrakhimova, A. I. 3 2021 Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations. Zbl 1468.35050Borisov, D. I.; Zezyulin, D. A.; Znojil, M. 2 2021 Bifurcations of essential spectra generated by a small non-Hermitian hole. I: Meromorphic continuations. Zbl 1479.35582Borisov, D. I.; Zezyulin, D. A. 1 2021 On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders. Zbl 1458.81018Borisov, D. I.; Golovina, A. M. 1 2021 Quantum graphs with small edges: holomorphy of resolvents. Zbl 1479.81026Borisov, D. I. 1 2021 On discrete spectrum of a model graph with loop and small edges. Zbl 1472.81069Borisov, D. I.; Konyrkulzhaeva, M. N.; Mukhametrakhimova, A. I. 1 2021 On a model graph with a loop and small edges. Holomorphy property of resolvent. Zbl 1458.34059Borisov, D. I.; Mukhametrakhimova, A. I. 4 2020 Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. Zbl 1427.81028Borisov, D. I.; Zezyulin, D. A. 3 2020 Asymptotic analysis of mean exit time for dynamical systems with a single well potential. Zbl 1441.35020Borisov, D.; Sultanov, O. 2 2020 Analytic continuation of resolvents of elliptic operators in a multidimensional cylinder. Zbl 07251966Borisov, D. I.; Golovina, A. M.; Mukhametrakhimova, A. I. 1 2020 Anomalous mechanisms of the loss of observability in non-Hermitian quantum models. Zbl 1473.81151Znojil, Miloslav; Borisov, Denis I. 1 2020 Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge. Zbl 1426.34039Borisov, D. I.; Konyrkulzhaeva, M. N. 4 2019 Gaps in the spectrum of the Laplacian in a strip with periodic delta interaction. Zbl 1430.35169Borisov, D. I. 2 2019 Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum. Zbl 1463.34127Borisov, Denis Ivanovich; Konyrkulzhaeva, Maral Nurlanovna 2 2019 Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip. Zbl 1432.35062Borisov, D. I. 1 2019 Estimates of initial scales for layers with small random negative-definite perturbations. Zbl 1440.60058Borisov, D. I. 1 2019 The norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes. Zbl 1403.35023Borisov, D. I.; Mukhametrakhimova, A. I. 8 2018 Two patterns of \(\mathcal{PT}\)-symmetry breakdown in a non-numerical six-state simulation. Zbl 1390.81172Znojil, Miloslav; Borisov, Denis I. 5 2018 Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip. Zbl 1405.35020Borisov, D. I. 3 2018 Expansion of the spectrum in the weak disorder regime for random operators in continuum space. Zbl 1386.35291Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 3 2018 Resonant interaction of \(\phi^4\) kink with \(\mathcal{PT}\)-symmetric perturbation with spatially periodic gain/loss coefficient. Zbl 07263227Saadatmand, Danial; Borisov, Denis I.; Kevrekidis, Panayotis G.; Zhou, Kun; Dmitriev, Sergey V. 2 2018 Spectral localization for quantum Hamiltonians with weak random delta interaction. (Localisation spectrale pour des hamiltoniens quantiques, avec une faible interaction aléatoire delta.) Zbl 1401.35218Borisov, Denis I.; Täufer, Matthias; Veselić, Ivan 1 2018 On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation. Zbl 1463.35386Borisov, Denis Ivanovich 1 2018 Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations. Zbl 1381.35027Borisov, Denis; Tautenhahn, Martin; Veselić, Ivan 6 2017 On eigenvalues of a \(\mathcal{PT}\)-symmetric operator in a thin layer. Zbl 1371.35178Borisov, Denis I.; Znojil, Miloslav 5 2017 On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation. Zbl 1364.35305Borisov, D. I.; Dmitriev, S. V. 5 2017 The spectrum of geodesic balls on spherically symmetric manifolds. Zbl 1380.53047Borisov, Denis; Freitas, Pedro 2 2017 Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve. Zbl 1361.35021Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 27 2016 Existence of the stationary solution of a Rayleigh-type equation. Zbl 1408.35118Borisov, D. I.; Gaydukov, R. K. 4 2016 On the resolvent of multidimensional operators with frequently alternating boundary conditions with the Robin homogenized condition. Zbl 1346.35054Borisov, D. I.; Sharapov, T. F. 4 2016 Quantum Hamiltonians with weak random abstract perturbation. I: Initial length scale estimate. Zbl 1348.82039Borisov, Denis; Golovina, Anastasia; Veselić, Ivan 3 2016 Expansion of the almost sure spectrum in the weak disorder regime. Zbl 1331.82026Borisov, Denis; Hoecker-Escuti, Francisco; Veselić, Ivan 2 2016 Creation of spectral bands for a periodic domain with small windows. Zbl 1342.81143Borisov, D. I. 1 2016 Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. Zbl 1402.81149Borisov, Denis I.; Znojil, Miloslav 1 2016 On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows. Zbl 1319.35134Borisov, D. I. 7 2015 Multiply degenerate exceptional points and quantum phase transitions. Zbl 1329.81037Borisov, Denis I.; Ružička, František; Znojil, Miloslav 4 2015 Kink scattering from a parity-time-symmetric defect in the \(\phi^4\) model. Zbl 07246123Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.; Fatykhov, Minnekhan A.; Javidan, Kurosh 4 2015 Multiscale unique continuation properties of eigenfunctions. Zbl 1337.35031Borisov, Denis; Nakić, Ivica; Rose, Christian; Tautenhahn, Martin; Veselić, Ivan 2 2015 Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators. Zbl 1339.81037Borisov, D.; Tautenhahn, M.; Veselić, I. 2 2015 Perturbation of threshold of essential spectrum for waveguides with windows. II: Asymptotics. Zbl 1335.35162Borisov, D. I. 1 2015 Norm-resolvent convergence for elliptic operators in domain with perforation along curve. Zbl 1304.35058Borisov, Denis; Cardone, Giuseppe; Durante, Tiziana 3 2014 Waveguide with non-periodically alternating Dirichlet and Robin conditions: Homogenization and asymptotics. Zbl 1282.35033Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 23 2013 Uniform resolvent convergence for strip with fast oscillating boundary. Zbl 1286.35025Borisov, Denis; Cardone, Giuseppe; Faella, Luisa; Perugia, Carmen 21 2013 Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones. Zbl 1269.81050Borisov, Denis; Pankrashkin, Konstantin 18 2013 Gap opening and split band edges in waveguides coupled by a periodic system of small windows. Zbl 1288.81046Borisov, D. I.; Pankrashkin, K. V. 15 2013 Low lying eigenvalues of randomly curved quantum waveguides. Zbl 1292.81051Borisov, Denis; Veselić, Ivan 9 2013 Tunneling resonances in systems without a classical trapping. Zbl 1280.81035Borisov, D.; Exner, P.; Golovina, A. 6 2013 Asymptotics for the expected lifetime of Brownian motion on thin domains in \(\mathbb R^n\). Zbl 1296.60220Borisov, Denis; Freitas, Pedro 5 2013 On the extrema of band functions in periodic waveguides. Zbl 1308.34111Borisov, D. I.; Pankrashkin, K. V. 5 2013 On a \(\mathcal{PT}\)-symmetric waveguide with a pair of small holes. Zbl 1321.47166Borisov, D. I. 5 2013 On the spectrum of deformations of compact double-sided flat hypersurfaces. Zbl 1282.35261Borisov, Denis; Freitas, Pedro 2 2013 The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions. Zbl 1241.47042Borisov, Denis; Krejčiřík, David 9 2012 Planar waveguide with “twisted” boundary conditions: small width. Zbl 1274.81108Borisov, Denis; Cardone, Giuseppe 6 2012 Homogenization and asymptotics for a waveguide with an infinite number of closely located small windows. Zbl 1290.81038Borisov, D.; Bunoiu, R.; Cardone, G. 12 2011 Planar waveguide with ”twisted” boundary conditions: Discrete spectrum. Zbl 1273.81100Borisov, Denis; Cardone, Giuseppe 9 2011 On the spectrum of a two-dimensional periodic operator with a small localized perturbation. Zbl 1233.35066Borisov, D. I. 9 2011 Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods. Zbl 1223.35248Borisov, Denis; Cardone, Giuseppe 9 2011 On a waveguide with an infinite number of small windows. (Sur un guide d’onde avec un nombre infini de petites fentes.) Zbl 1211.35098Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 9 2011 Low lying spectrum of weak-disorder quantum waveguides. Zbl 1208.82089Borisov, Denis; Veselić, Ivan 8 2011 Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in \(\mathbb R^d\). Zbl 1180.35397Borisov, Denis; Freitas, Pedro 29 2010 On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition. Zbl 1210.82077Borisov, Denis; Bunoiu, Renata; Cardone, Giuseppe 22 2010 Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Zbl 1168.35401Borisov, Denis; Freitas, Pedro 26 2009 Homogenization of the planar waveguide with frequently alternating boundary conditions. Zbl 1178.81088Borisov, D.; Cardone, G. 26 2009 Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation. Zbl 1181.35151Borisov, Denis; Freitas, Pedro 12 2009 Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Zbl 1206.35029Borisov, D. 11 2009 \(\mathcal {PT}\)-symmetric waveguides. Zbl 1178.35141Borisov, Denis; Krejčiřík, David 22 2008 On the spectrum of a periodic operator with a small localized perturbation. Zbl 1169.34056Borisov, D. I.; Gadyl’shin, R. R. 16 2008 Distant perturbations of the Laplacian in a multi-dimensional space. Zbl 1143.35075Borisov, Denis I. 14 2007 Asymptotic behaviour of the spectrum of a waveguide with distant perturbations. Zbl 1185.35155Borisov, Denis 14 2007 The spectrum of two quantum layers coupled by a window. Zbl 1115.81024Borisov, D. 8 2007 Some singular perturbations of periodic operators. Zbl 1147.34060Borisov, D. I. 7 2007 The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis. Zbl 1137.34039Borisov, D. I.; Gadyl’shin, R. R. 4 2007 The spectrum of a periodic operator with a small localized perturbation. Zbl 1175.34106Borisov, D. I.; Gadyl’shin, R. R. 1 2007 Discrete spectrum of an asymmetric pair of waveguides coupled through a window. Zbl 1156.35066Borisov, D. I. 29 2006 Distant perturbation asymptotics in window-coupled waveguides. I: The nonthreshold case. Zbl 1112.81043Borisov, D.; Exner, P. 10 2006 The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Zbl 1177.34107Borisov, D. I.; Gadyl’shin, R. R. 6 2006 On the spectrum of the Schrödinger operator perturbed by a rapidly oscillating potential. Zbl 1134.34337Borisov, D. I. 2 2006 On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets. Zbl 1210.34071Borisov, D. I. 2 2006 Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions. Zbl 1077.81038Borisov, Denis; Ekholm, Tomas; Kovařík, Hynek 11 2005 Discrete spectrum of the Schrödinger operator perturbed by a narrowly supported potential. Zbl 1178.35144Bikmetov, A. R.; Borisov, D. I. 1 2005 Exponential splitting of bound states in a waveguide with a pair of distant windows. Zbl 1050.81008Borisov, D.; Exner, P. 20 2004 Asymptotics and estimates of the convergence rate in a three-dimensional boundary value problem with rapidly alternating boundary conditions. Zbl 1108.35032Borisov, D. I. 3 2004 On a model boundary value problem for Laplacian with frequently alternating type of boundary condition. Zbl 1137.35308Borisov, Denis I. 16 2003 Asymptotics and estimates for the eigenelements of the Laplacian with frequent nonperiod change of boundary conditions. Zbl 1067.35055Borisov, D. I. 8 2003 Geometric coupling thresholds in a two-dimensional strip. Zbl 1060.35094Borisov, D.; Exner, P.; Gadyl’shin, R. 26 2002 Boundary-value problem in a cylinder with frequently changing type of boundary conditions. Zbl 1045.35047Borisov, D. I. 4 2002 On a Laplacian with frequently nonperiodically alternating boundary conditions. Zbl 1197.35027Borisov, D. I. 2 2002 On a singularly perturbed boundary value problem for the Laplacian in a cylinder. Zbl 1274.35013Borisov, D. I. 1 2002 Bound states in weakly deformed strips and layers. Zbl 1043.35046Borisov, D.; Exner, P.; Gadyl’shin, R.; Krejčiřík, D. 27 2001 Two-parameter asymptotics in a boundary value problem for the Laplacian. Zbl 1140.35544Borisov, D. I. 4 2001 On the spectrum of the Laplacian with frequently alternating boundary conditions. Zbl 0945.35066Borisov, D. I.; Gadyl’shin, R. R. 3 1999 all cited Publications top 5 cited Publications all top 5 Cited by 237 Authors 67 Borisov, Denis Ivanovich 32 Nazarov, Sergeĭ Aleksandrovich 18 Cardone, Giuseppe 15 Krejčiřík, David 13 Veselić, Ivan 9 Golovina, Anastasiya Mihajlovna 8 Chechkin, Gregory Aleksandrovich 8 Exner, Pavel 8 Gadyl’shin, Rustem R. 7 Siegl, Petr 6 Freitas, Pedro 6 Khrabustovskyi, Andrii 6 Khusnullin, Il’fat Khamzievich 6 Weinstein, Michael I. 6 Yang, Chuanfu 5 Bikmetov, Aĭdar Renatovich 5 Drouot, Alexis 5 Konyrkulzhaeva, Maral Nurlanovna 5 Mukhametrakhimova, A. I. 5 Trynin, Aleksandr Yur’evich 4 Bunoiu, Renata 4 Gaydukov, R. K. 4 Kovařík, Hynek 4 Lotoreichik, Vladimir 4 Najar, Hatem 4 Pankrashkin, Konstantin 4 Pérez-martínez, María-eugenia 4 Taskinen, Jari 4 Täufer, Matthias 4 Tautenhahn, Martin 4 Verri, Alessandra A. 4 Znojil, Miloslav 3 Beck, Thomas L. 3 Buttazzo, Giuseppe 3 Chechkina, Aleksandra Grigorievna 3 De Maio, Umberto 3 de Oliveira, César R. 3 Durante, Tiziana 3 Fefferman, Charles Louis 3 Gómez, Delfina 3 Grushin, V. V. 3 Pažanin, Igor 3 Popov, Igor’ Yur’evich 3 Raymond, Nicolas 3 Royer, Julien 3 Ruotsalainen, Keijo Matti 3 Senik, Nikita N. 3 Shaposhnikova, Tatiana A. 3 Siudeja, Bartłomiej Andrzej 3 Suslina, Tat’yana Aleksandrovna 3 Zezyulin, Dmitry A. 2 Aiyappan, Srinivasan 2 Alonso Izquierdo, A. Alonso 2 Bakharev, Fedor L’vovich 2 Behrndt, Jussi 2 Briani, Luca 2 Briet, Philippe 2 D’Apice, Ciro 2 Duchêne, Vincent 2 Ekholm, Tomas 2 Faella, Luisa 2 Hıra, Fatma 2 Hoecker-Escuti, Francisco 2 Kondej, Sylwia 2 Koroleva, Yulia O. 2 Langer, Matthias 2 Laugesen, Richard Snyder 2 Lee-Thorp, James P. 2 Lu, Jianfeng 2 Marušić-Paloka, Eduard 2 Marzuola, Jeremy Louis 2 Mascarenhas, Maria-Luisa 2 Nieto, Luis Miguel 2 Orive Illera, Rafael 2 Perugia, Carmen 2 Piatnitski, Andrey L. 2 Plum, Michael 2 Podolskii, Alexander V. 2 Prinari, Francesca 2 Queiroga-Nunes, J. 2 Raikov, Georgi D. 2 Rybalko, Yan 2 Sharapov, Timur Farkhatovich 2 Shepelsky, Dmitry 2 Uusitalo, Pauliina 2 Vukićević, Iva 2 Wang, Juan 2 Watson, Alexander B. 2 Železný, Jakub 2 Zhao, Jie 1 Akbarfam, Aliasghar Jodayree 1 Akhmetgaliyev, Eldar 1 Alkhutov, Yuriy Alexandrovich 1 Altinisik, Nihat 1 Amirat, Youcef Aït 1 Amore, Paolo 1 Anné, Colette 1 Bao, Gang 1 Barrera-Figueroa, Victor 1 Barseghyan, Diana ...and 137 more Authors all top 5 Cited in 103 Serials 28 Journal of Mathematical Sciences (New York) 17 Journal of Mathematical Physics 13 Journal of Mathematical Analysis and Applications 13 Journal of Differential Equations 8 Mathematical Notes 8 Russian Journal of Mathematical Physics 8 St. Petersburg Mathematical Journal 7 Journal of Functional Analysis 7 SIAM Journal on Mathematical Analysis 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Theoretical and Mathematical Physics 6 Ufimskiĭ Matematicheskiĭ Zhurnal 5 Applicable Analysis 5 Journal of Statistical Physics 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Annales Henri Poincaré 5 Journal of Spectral Theory 4 Reports on Mathematical Physics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Doklady Mathematics 4 Mathematical Physics, Analysis and Geometry 4 Communications in Contemporary Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Proceedings of the Steklov Institute of Mathematics 4 Analysis and Mathematical Physics 3 Communications in Mathematical Physics 3 Letters in Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Journal of Computational and Applied Mathematics 3 Transactions of the American Mathematical Society 3 Computational Mathematics and Mathematical Physics 3 Sbornik: Mathematics 3 European Journal of Mechanics. B. Fluids 3 Inverse Problems in Science and Engineering 3 Journal of Physics A: Mathematical and Theoretical 2 International Journal of Theoretical Physics 2 Applied Mathematics and Optimization 2 Integral Equations and Operator Theory 2 Mathematika 2 Memoirs of the American Mathematical Society 2 Siberian Mathematical Journal 2 Transactions of the Moscow Mathematical Society 2 Asymptotic Analysis 2 SIAM Journal on Applied Mathematics 2 Calculus of Variations and Partial Differential Equations 2 Journal of Inequalities and Applications 2 Communications in Nonlinear Science and Numerical Simulation 2 Differential Equations 2 Pure and Applied Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Computational Physics 1 Nuclear Physics. B 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Reviews in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal of the London Mathematical Society. Second Series 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Ricerche di Matematica 1 SIAM Journal on Control and Optimization 1 Studies in Applied Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Physica D 1 Journal of Theoretical Probability 1 Applied Mathematics Letters 1 The Journal of Geometric Analysis 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Russian Mathematics 1 Filomat 1 Izvestiya: Mathematics 1 Mathematical Problems in Engineering 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 1 Annals of Mathematics. Second Series 1 Acta Mathematica Sinica. English Series 1 The ANZIAM Journal 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Journal of Mathematical Physics, Analysis, Geometry 1 Complex Variables and Elliptic Equations 1 Complex Analysis and Operator Theory 1 Networks and Heterogeneous Media 1 Advances in High Energy Physics 1 Advances in Calculus of Variations 1 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 1 Journal of Pseudo-Differential Operators and Applications 1 Eurasian Mathematical Journal 1 Azerbaijan Journal of Mathematics ...and 3 more Serials all top 5 Cited in 30 Fields 216 Partial differential equations (35-XX) 91 Quantum theory (81-XX) 74 Operator theory (47-XX) 41 Ordinary differential equations (34-XX) 27 Statistical mechanics, structure of matter (82-XX) 21 Optics, electromagnetic theory (78-XX) 17 Mechanics of deformable solids (74-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Global analysis, analysis on manifolds (58-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Approximations and expansions (41-XX) 7 Numerical analysis (65-XX) 7 Fluid mechanics (76-XX) 6 Probability theory and stochastic processes (60-XX) 4 Differential geometry (53-XX) 3 Combinatorics (05-XX) 3 Algebraic geometry (14-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Number theory (11-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Relativity and gravitational theory (83-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year