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Laptev, Ari

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Author ID: laptev.ari Recent zbMATH articles by "Laptev, Ari"
Published as: Laptev, Ari; Laptev, A.; Laptev, A. A.; Laptev, Ari A.
Homepage: http://wwwf.imperial.ac.uk/~alaptev/
External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · dblp · GND · IdRef · theses.fr
Documents Indexed: 132 Publications since 1974, including 10 Books
Biographic References: 3 Publications
all top 5

Co-Authors

24 single-authored
11 Naboko, Serguei N.
10 Safronov, Oleg
9 Ilyin, Alexei A.
8 Dolbeault, Jean
8 Esteban, Maria J.
8 Loss, Michael
8 Safarov, Yuri G.
7 Birman, Mikhail Shlëmovich
7 Frank, Rupert L.
7 Kurasov, Pavel B.
6 Weidl, Timo
5 Solomyak, Mikhaĭl Zakharovich
5 Zelik, Sergey V.
4 Hoffmann-Ostenhof, Thomas
4 Janas, Jan
4 Kovařík, Hynek
4 Suslina, Tat’yana Aleksandrovna
3 Simon, Barry
3 Sobolev, Alexander V.
3 Stolz, Gunter
3 Yafaev, Dimitri R.
2 Bonheure, Denis
2 Dittrich, Jaroslav
2 Faddeev, Lyudvig Dmitrievich
2 Ferrulli, Francesco
2 Gesztesy, Fritz
2 Hoffmann-Ostenhof, Maria
2 Korotyaev, Evgeny L.
2 Mitrea, Marius
2 Molchanov, Stanislav Alekseevich
2 Östensson, Jörgen
2 Schimmer, Lukas
2 Seiringer, Robert
2 Shterenberg, Roman G.
2 Sukhtaiev, Selim
2 Takhtajan, Leon Armenovich
2 Ural’tseva, Nina Nikolaevna
2 Velicu, Andrei
2 Vershik, Anatoliĭ Moiseevich
1 Aermark, L.
1 Aksent’ev, Leonid Aleksandrovich
1 Aptekarev, Alexander Ivanovich
1 Ashbaugh, Mark S.
1 Avkhadiev, Farit Gabidinovich
1 Babich, Vasiliĭ Mikhaĭlovich
1
1 Bikchentaev, Aĭrat Midkhatovich
1 Bourguignon, Jean-Pierre
1 Bühlmann, Peter
1 Buslaev, Vladimir Savel’evich
1 Chanillo, Sagun
1 Cuenin, Jean-Claude
1 Dubinin, Vladimir N.
1 Ekholm, Tomas
1 Elizarov, A. M.
1 Exner, Pavel
1 Fanelli, Luca
1 Geisinger, Leander
1 Gindikin, Simon Grigorevich
1 Glushkin, E. D.
1 Gordon, Alexander Ya.
1 Goryainov, Viktor V.
1 Guzu, Dorian
1 Hansson, Anders M.
1 Hassannezhad, Asma
1 Khavin, Viktor Petrovich
1 Helffer, Bernard
1 Hundertmark, Dirk
1 Its, Alexander Rudolfovich
1 Kapitanski, Lev
1 Kislyakov, Sergeĭ Vital’evich
1 Kozlov, Vladimir A.
1 Krejčiřík, David
1 Langmann, Edwin
1 Lieb, Elliott H.
1 Maad Sasane, Sara
1 Makarov, Boris M.
1 Marchenko, Vladimir Aleksandrovich
1 Mityagin, Boris Samuilovich
1 Nasyrov, S. R.
1 Natalini, Roberto
1 Nevai, Paul G.
1 Nikol’skiĭ, Nikolaĭ Kapitonovich
1 Pastur, Leonid Andreevich
1 Paufler, Cornelius
1 Peicheva, Anastasiya S.
1 Plamenevskiĭ, Boris Alekseevich
1 Portmann, Fabian
1 Prokhorov, Dmitriĭ Vladimirovich
1 Robert, Didier
1 Ruzhansky, Michael V.
1 Salinger, David L.
1 Sergeev, Armen Glebovich
1 Shlapunov, Aleksandr Anatol’evich
1 Sigal, Israel Michael
1 Stepanov, Vladimir Dmitrievich
1 Stuart, Andrew M.
1 Tarasov, Vitaly Olegovich
1 Tidblom, Jesper
1 Tretter, Christiane
...and 3 more Co-Authors
all top 5

Serials

8 Journal of Functional Analysis
6 Communications in Mathematical Physics
5 St. Petersburg Mathematical Journal
5 Operator Theory: Advances and Applications
4 Russian Mathematical Surveys
3 Journal of Mathematical Physics
3 Journal of the London Mathematical Society. Second Series
3 IMRN. International Mathematics Research Notices
3 Problemy Matematicheskogo Analiza
3 European Mathematical Society Newsletter
3 Journal of Spectral Theory
2 Communications on Pure and Applied Mathematics
2 Mathematical Notes
2 Arkiv för Matematik
2 Reviews in Mathematical Physics
2 Functional Analysis and its Applications
2 Proceedings of the American Mathematical Society
2 Journal of Mathematical Sciences (New York)
2 Annales Henri Poincaré
2 Bulletin of Mathematical Sciences
1 Inverse Problems
1 Journal of Mathematical Analysis and Applications
1 Journal of Statistical Physics
1 Letters in Mathematical Physics
1 Matematicheskie Zametki
1 Nonlinearity
1 Acta Mathematica
1 Advances in Mathematics
1 Gazette des Mathématiciens
1 Inventiones Mathematicae
1 Journal of Soviet Mathematics
1 Mathematische Nachrichten
1 Mathematica Scandinavica
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Soviet Mathematics. Doklady
1 Transactions of the Moscow Mathematical Society
1 Trudy Moskovskogo Matematicheskogo Obshchestva
1 Asymptotic Analysis
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Geometric and Functional Analysis. GAFA
1 Communications in Partial Differential Equations
1 Journal of Physics A: Mathematical and General
1 Mathematical Research Letters
1 Sbornik: Mathematics
1 Doklady Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Communications in Contemporary Mathematics
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Journal of Mathematical Physics, Analysis, Geometry
1 Complex Variables and Elliptic Equations
1 Complex Analysis and Operator Theory
1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova
1 Analysis & PDE
1 Wiadomości Matematyczne
1 Analysis and Mathematical Physics
1 EMS Series of Congress Reports

Publications by Year

Citations contained in zbMATH Open

88 Publications have been cited 924 times in 579 Documents Cited by Year
Sharp Lieb-Thirring inequalities in high dimensions. Zbl 1142.35531
Laptev, Ari; Weidl, Timo
70
2000
Hardy inequalities for magnetic Dirichlet forms. Zbl 0977.26005
Laptev, Ari; Weidl, Timo
56
1999
Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. Zbl 0892.35115
Laptev, A.
53
1997
A geometrical version of Hardy’s inequality. Zbl 1012.26011
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.
46
2002
Eigenvalue estimates for Schrödinger operators with complex potentials. Zbl 1185.35045
Laptev, Ari; Safronov, Oleg
43
2009
Recent results on Lieb-Thirring inequalities. Zbl 1135.81337
Laptev, Ari; Weidl, Timo
42
2000
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
40
2006
Lieb-Thirring inequalities with improved constants. Zbl 1152.35451
Dolbeault, Jean; Laptev, Ari; Loss, Michael
33
2008
On new relations between spectral properties of Jacobi matrices and their coefficients. Zbl 1135.47303
Laptev, A.; Naboko, S.; Safronov, O.
25
2003
The negative discrete spectrum of a two-dimensional Schrödinger operator. Zbl 0864.35080
Birman, M. Sh.; Laptev, A.
24
1996
New bounds on the Lieb-Thirring constants. Zbl 1074.35569
Hundertmark, D.; Laptev, A.; Weidl, T.
24
2000
Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials. Zbl 1077.81040
Laptev, A.; Naboko, S.; Safronov, O.
22
2005
One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows. Zbl 1320.26017
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
21
2014
Hardy inequalities for nonconvex domains. Zbl 1183.26017
Avkhadiev, Farit; Laptev, Ari
20
2010
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
20
2016
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line. Zbl 1287.81050
Cuenin, Jean-Claude; Laptev, Ari; Tretter, Christiane
18
2014
Szegö type limit theorems. Zbl 0878.47020
Laptev, A.; Safarov, Yu.
16
1996
Generalized Hardy inequality for the magnetic Dirichlet forms. Zbl 1127.26015
Balinsky, Alexander; Laptev, Ari; Sobolev, Alexander V.
16
2004
Geometrical versions of improved Berezin-Li-Yau inequalities. Zbl 1257.35138
Geisinger, Leander; Laptev, Ari; Weidl, Timo
16
2011
Spectral estimates on the sphere. Zbl 1293.35183
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari
15
2014
Many-particle Hardy inequalities. Zbl 1135.35012
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.; Tidblom, J.
14
2008
Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
14
2016
Discrete spectrum of the perturbed Dirac operator. Zbl 0822.35104
Birman, Mikhail Sh.; Laptev, Ari
12
1994
Nonlinear eigenvalues and analytic hypoellipticity. Zbl 1053.35045
Chanillo, Sagun; Helffer, Bernard; Laptev, Ari
12
2004
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
12
2011
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates. Zbl 1276.58007
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
10
2013
Global Fourier integral operators and semiclassical asymptotics. Zbl 0962.35201
Laptev, A.; Sigal, I. M.
9
2000
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
Hardy inequalities with homogeneous weights. Zbl 1322.35103
Hoffmann-Ostenhof, Thomas; Laptev, Ari
8
2015
Hardy inequalities for Robin Laplacians. Zbl 1242.26022
Kovařík, Hynek; Laptev, Ari
8
2012
Hardy inequalities for simply connected planar domains. Zbl 1168.26003
Laptev, Ari; Sobolev, Alexander V.
8
2008
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
8
2013
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
A Szegő condition for a multidimensional Schrödinger operator. Zbl 1135.35355
Laptev, A.; Naboko, S.; Safronov, O.
7
2005
Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices. Zbl 1403.39017
Korotyaev, Evgeny; Laptev, Ari
7
2018
On global representations of Lagrangian distributions and solutions of hyperbolic equations. Zbl 0811.35177
Laptev, A.; Safarov, Yu.; Vassiliev, D.
6
1994
A generalization of the Berezin-Lieb inequality. Zbl 0868.47016
Laptev, A.; Safarov, Yu.
6
1996
Solitons and the removal of eigenvalues for fourth-order differential operators. Zbl 1123.34067
Hoppe, J.; Laptev, A.; Östensson, J.
6
2006
On the negative eigenvalues of a class of Schrödinger operators. Zbl 0941.35055
Laptev, A.; Netrusov, Yu.
6
1999
Bound state asymptotics for elliptic operators with strongly degenerated symbols. Zbl 1045.35049
Laptev, Ari; Safronov, Oleg; Weidl, Timo
6
2002
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field. Zbl 1238.35014
Aermark, L.; Laptev, Ari
6
2012
Spectral asymptotics of a certain class of Fourier integral operators. Zbl 0503.47044
Laptev, A. A.
5
1981
On the Lieb-Thirring conjecture for a class of potentials. Zbl 0938.35112
Laptev, Ari
5
1999
The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
5
1997
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Sharp spectral inequalities for the Heisenberg Laplacian. Zbl 1157.58008
Hansson, A. M.; Laptev, Ari
5
2008
On some sharp spectral inequalities for Schrödinger operators on semiaxis. Zbl 1297.35155
Exner, Pavel; Laptev, Ari; Usman, Muhammad
5
2014
Magnetic rings. Zbl 1390.81142
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
5
2018
Discrete spectrum of the perturbed Dirac operator. Zbl 0858.47004
Birman, M. Sh.; Laptev, A.
4
1994
The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius. Zbl 0972.35079
Laptev, A.
4
2000
On an estimate of the remainder term in formulas of the spectral asymptotics for one class of integral operators. Zbl 0443.47051
Laptev, A. A.
4
1977
Asymptotics of the negative discrete spectrum of a class of Schrödinger operators with large coupling constant. Zbl 0795.35071
Laptev, Ari
3
1993
Remarks on the paper of V. Guillemin and K. Okikiolu: “Subprincipal terms in Szegő estimates”. Zbl 0917.58046
Laptev, A.; Robert, D.; Safarov, Yu.
3
1998
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
3
2010
Hardy inequalities for \(p\)-Laplacians with Robin boundary conditions. Zbl 1360.47008
Ekholm, Tomas; Kovařík, Hynek; Laptev, Ari
3
2015
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
3
2016
Interpolation inequalities and spectral estimates for magnetic operators. Zbl 1388.81104
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2018
On estimates of singular numbers for a class of integral operators. Zbl 0478.47032
Laptev, A. A.
2
1981
Spectral asymptotics of a class of Fourier integral operators. Zbl 0535.47030
Laptev, A. A.
2
1983
Spectral asymptotic behavior of a class of integral operators. Zbl 0322.45003
Laptev, A. A.
2
1975
Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. I. Zbl 1428.26029
Laptev, Ari; Ruzhansky, Michael; Yessirkegenov, Nurgissa
2
2019
On the improvement of the Hardy inequality due to singular magnetic fields. Zbl 1450.35011
Fanelli, Luca; Krejčiřík, David; Laptev, Ari; Vega, Luis
2
2020
A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions. Zbl 1362.35197
Ashbaugh, Mark S.; Gesztesy, Fritz; Laptev, Ari; Mitrea, Marius; Sukhtaiev, Selim
2
2017
Reflectionless potentials for an ordinary differential operator of order four. Zbl 1103.34071
Laptev, A.; Shterenberg, R.; Sukhanov, V.; Östensson, J.
2
2006
Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. I: Semibounded gap. Zbl 1070.47041
Birman, M. Sh.; Laptev, A.; Suslina, T. A.
2
2001
Inverse spectral problems for Schrödinger operators with energy depending potentials. Zbl 1146.35095
Laptev, A.; Shterenberg, R.; Sukhanov, V.
2
2007
Spectral inequalities for partial differential equations and their applications. Zbl 1269.35050
Laptev, Ari
2
2012
Finding eigenvalues and eigenfunctions of the Zaremba problem for the circle. Zbl 1367.47052
Laptev, Ari; Peicheva, Anastasiya; Shlapunov, Alexander
2
2017
The negative discrete spectrum of a class of two-dimensional Schrödinger operators with magnetic fields. Zbl 1083.35070
Laptev, A.; Safronov, O.
2
2005
Eigenvalues of the bilayer graphene operator with a complex valued potential. Zbl 1429.81034
Safronov, Oleg; Laptev, Ari; Ferrulli, Francesco
1
2019
Error estimate in the generalized Szegö theorem. Zbl 0743.58032
Laptev, A.; Safarov, Yu.
1
1991
On inequalities for the bound states of Schrödinger operators. Zbl 0833.35032
Laptev, A.
1
1995
Spectral asymptotics of a composition of pseudodifferential operators and reflections from the boundary. Zbl 0391.47035
Laptev, A. A.
1
1977
Spectral inequalities for a class of integral operators. Zbl 07139970
Laptev, A.; Velicu, A.
1
2019
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
Eigenvalue bounds of mixed Steklov problems. Zbl 1442.35280
Hassannezhad, Asma; Laptev, Ari
1
2020
Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields. Zbl 1439.81049
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
1
2020
Operator methods in mathematical physics. Conference on operator theory, analysis and mathematical physics (OTAMP) 2010, Bedlewo, Poland. Zbl 1257.00017
Janas, Jan (ed.); Kurasov, Pavel (ed.); Laptev, Ari (ed.); Naboko, Sergei (ed.)
1
2013
Trace formulas for a discrete Schrödinger operator. Zbl 06835370
Korotyaev, E. L.; Laptev, A.
1
2017
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
1
2010
On continuous and discrete Hardy inequalities. Zbl 1368.35010
Kapitanski, Lev; Laptev, Ari
1
2016
Functional analysis and operator theory for quantum physics. The Pavel Exner anniversary volume. Dedicated to Pavel Exner on the occasion of his 70th birthday. Zbl 1364.46005
Dittrich, Jaroslav (ed.); Kovařík, Hynek (ed.); Laptev, Ari (ed.)
1
2017
Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder. Zbl 1355.81085
Laptev, Ari; Maad Sasane, Sara
1
2017
A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets. Zbl 1339.35202
Gesztesy, F.; Mitrea, M.; Sukhtaiev, S.; Laptev, A.
1
2015
“Non-standard” spectral asymptotics for a two-dimensional Schrödinger operator. Zbl 0910.35086
Birman, Mikhail Sh.; Laptev, Ari
1
1997
On the improvement of the Hardy inequality due to singular magnetic fields. Zbl 1450.35011
Fanelli, Luca; Krejčiřík, David; Laptev, Ari; Vega, Luis
2
2020
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
Eigenvalue bounds of mixed Steklov problems. Zbl 1442.35280
Hassannezhad, Asma; Laptev, Ari
1
2020
Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields. Zbl 1439.81049
Bonheure, Denis; Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
1
2020
Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. I. Zbl 1428.26029
Laptev, Ari; Ruzhansky, Michael; Yessirkegenov, Nurgissa
2
2019
Eigenvalues of the bilayer graphene operator with a complex valued potential. Zbl 1429.81034
Safronov, Oleg; Laptev, Ari; Ferrulli, Francesco
1
2019
Spectral inequalities for a class of integral operators. Zbl 07139970
Laptev, A.; Velicu, A.
1
2019
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Trace formulae for Schrödinger operators with complex-valued potentials on cubic lattices. Zbl 1403.39017
Korotyaev, Evgeny; Laptev, Ari
7
2018
Magnetic rings. Zbl 1390.81142
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
5
2018
Interpolation inequalities and spectral estimates for magnetic operators. Zbl 1388.81104
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
3
2018
A bound for the eigenvalue counting function for Krein-von Neumann and Friedrichs extensions. Zbl 1362.35197
Ashbaugh, Mark S.; Gesztesy, Fritz; Laptev, Ari; Mitrea, Marius; Sukhtaiev, Selim
2
2017
Finding eigenvalues and eigenfunctions of the Zaremba problem for the circle. Zbl 1367.47052
Laptev, Ari; Peicheva, Anastasiya; Shlapunov, Alexander
2
2017
Trace formulas for a discrete Schrödinger operator. Zbl 06835370
Korotyaev, E. L.; Laptev, A.
1
2017
Functional analysis and operator theory for quantum physics. The Pavel Exner anniversary volume. Dedicated to Pavel Exner on the occasion of his 70th birthday. Zbl 1364.46005
Dittrich, Jaroslav; Kovařík, Hynek; Laptev, Ari
1
2017
Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder. Zbl 1355.81085
Laptev, Ari; Maad Sasane, Sara
1
2017
On the number of eigenvalues of Schrödinger operators with complex potentials. Zbl 1358.35074
Frank, Rupert L.; Laptev, Ari; Safronov, Oleg
20
2016
Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004
Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A.
14
2016
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
3
2016
On continuous and discrete Hardy inequalities. Zbl 1368.35010
Kapitanski, Lev; Laptev, Ari
1
2016
Hardy inequalities with homogeneous weights. Zbl 1322.35103
Hoffmann-Ostenhof, Thomas; Laptev, Ari
8
2015
Hardy inequalities for \(p\)-Laplacians with Robin boundary conditions. Zbl 1360.47008
Ekholm, Tomas; Kovařík, Hynek; Laptev, Ari
3
2015
A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets. Zbl 1339.35202
Gesztesy, F.; Mitrea, M.; Sukhtaiev, S.; Laptev, A.
1
2015
One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows. Zbl 1320.26017
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
21
2014
Eigenvalue estimates for non-selfadjoint Dirac operators on the real line. Zbl 1287.81050
Cuenin, Jean-Claude; Laptev, Ari; Tretter, Christiane
18
2014
Spectral estimates on the sphere. Zbl 1293.35183
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari
15
2014
On some sharp spectral inequalities for Schrödinger operators on semiaxis. Zbl 1297.35155
Exner, Pavel; Laptev, Ari; Usman, Muhammad
5
2014
Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates. Zbl 1276.58007
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
10
2013
On spectral estimates for two-dimensional Schrödinger operators. Zbl 1294.35048
Laptev, Ari; Solomyak, Michael
8
2013
Operator methods in mathematical physics. Conference on operator theory, analysis and mathematical physics (OTAMP) 2010, Bedlewo, Poland. Zbl 1257.00017
Janas, Jan; Kurasov, Pavel; Laptev, Ari; Naboko, Sergei
1
2013
On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. Zbl 1253.35037
Laptev, A.; Solomyak, M.
10
2012
Hardy inequalities for Robin Laplacians. Zbl 1242.26022
Kovařík, Hynek; Laptev, Ari
8
2012
Hardy inequalities for a magnetic Grushin operator with Aharonov-Bohm type magnetic field. Zbl 1238.35014
Aermark, L.; Laptev, Ari
6
2012
Spectral inequalities for partial differential equations and their applications. Zbl 1269.35050
Laptev, Ari
2
2012
Geometrical versions of improved Berezin-Li-Yau inequalities. Zbl 1257.35138
Geisinger, Leander; Laptev, Ari; Weidl, Timo
16
2011
A sharp bound on eigenvalues of Schrödinger operators on the half-line with complex-valued potentials. Zbl 1253.35086
Frank, Rupert L.; Laptev, Ari; Seiringer, Robert
12
2011
Hardy inequalities for nonconvex domains. Zbl 1183.26017
Avkhadiev, Farit; Laptev, Ari
20
2010
Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Zbl 1198.35161
Frank, Rupert L.; Laptev, Ari
3
2010
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
1
2010
Eigenvalue estimates for Schrödinger operators with complex potentials. Zbl 1185.35045
Laptev, Ari; Safronov, Oleg
43
2009
Lieb-Thirring inequalities with improved constants. Zbl 1152.35451
Dolbeault, Jean; Laptev, Ari; Loss, Michael
33
2008
Many-particle Hardy inequalities. Zbl 1135.35012
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.; Tidblom, J.
14
2008
Hardy inequalities for simply connected planar domains. Zbl 1168.26003
Laptev, Ari; Sobolev, Alexander V.
8
2008
Spectral inequalities for Schrödinger operators with surface potentials. Zbl 1170.35486
Frank, Rupert L.; Laptev, Ari
6
2008
Eigenvalue estimates for magnetic Schrödinger operators in domains. Zbl 1186.35119
Frank, Rupert L.; Laptev, Ari; Molchanov, Stanislav
5
2008
Sharp spectral inequalities for the Heisenberg Laplacian. Zbl 1157.58008
Hansson, A. M.; Laptev, Ari
5
2008
Inverse spectral problems for Schrödinger operators with energy depending potentials. Zbl 1146.35095
Laptev, A.; Shterenberg, R.; Sukhanov, V.
2
2007
Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Zbl 1160.81382
Frank, Rupert L.; Laptev, Ari; Lieb, Elliott H.; Seiringer, Robert
40
2006
Solitons and the removal of eigenvalues for fourth-order differential operators. Zbl 1123.34067
Hoppe, J.; Laptev, A.; Östensson, J.
6
2006
Reflectionless potentials for an ordinary differential operator of order four. Zbl 1103.34071
Laptev, A.; Shterenberg, R.; Sukhanov, V.; Östensson, J.
2
2006
Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials. Zbl 1077.81040
Laptev, A.; Naboko, S.; Safronov, O.
22
2005
A Szegő condition for a multidimensional Schrödinger operator. Zbl 1135.35355
Laptev, A.; Naboko, S.; Safronov, O.
7
2005
The negative discrete spectrum of a class of two-dimensional Schrödinger operators with magnetic fields. Zbl 1083.35070
Laptev, A.; Safronov, O.
2
2005
Generalized Hardy inequality for the magnetic Dirichlet forms. Zbl 1127.26015
Balinsky, Alexander; Laptev, Ari; Sobolev, Alexander V.
16
2004
Nonlinear eigenvalues and analytic hypoellipticity. Zbl 1053.35045
Chanillo, Sagun; Helffer, Bernard; Laptev, Ari
12
2004
On new relations between spectral properties of Jacobi matrices and their coefficients. Zbl 1135.47303
Laptev, A.; Naboko, S.; Safronov, O.
25
2003
A geometrical version of Hardy’s inequality. Zbl 1012.26011
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Laptev, A.
46
2002
Bound state asymptotics for elliptic operators with strongly degenerated symbols. Zbl 1045.35049
Laptev, Ari; Safronov, Oleg; Weidl, Timo
6
2002
Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. I: Semibounded gap. Zbl 1070.47041
Birman, M. Sh.; Laptev, A.; Suslina, T. A.
2
2001
Sharp Lieb-Thirring inequalities in high dimensions. Zbl 1142.35531
Laptev, Ari; Weidl, Timo
70
2000
Recent results on Lieb-Thirring inequalities. Zbl 1135.81337
Laptev, Ari; Weidl, Timo
42
2000
New bounds on the Lieb-Thirring constants. Zbl 1074.35569
Hundertmark, D.; Laptev, A.; Weidl, T.
24
2000
Global Fourier integral operators and semiclassical asymptotics. Zbl 0962.35201
Laptev, A.; Sigal, I. M.
9
2000
The negative spectrum of a class of two-dimensional Schrödinger operators with potentials depending only on radius. Zbl 0972.35079
Laptev, A.
4
2000
Hardy inequalities for magnetic Dirichlet forms. Zbl 0977.26005
Laptev, Ari; Weidl, Timo
56
1999
On the negative eigenvalues of a class of Schrödinger operators. Zbl 0941.35055
Laptev, A.; Netrusov, Yu.
6
1999
On the Lieb-Thirring conjecture for a class of potentials. Zbl 0938.35112
Laptev, Ari
5
1999
On the eigenvalue behaviour for a class of differential operators on the semiaxis. Zbl 0916.34067
Birman, M. Sh.; Laptev, A.; Solomyak, M.
9
1998
Remarks on the paper of V. Guillemin and K. Okikiolu: “Subprincipal terms in Szegő estimates”. Zbl 0917.58046
Laptev, A.; Robert, D.; Safarov, Yu.
3
1998
Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. Zbl 0892.35115
Laptev, A.
53
1997
The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). Zbl 0876.35079
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael
5
1997
“Non-standard” spectral asymptotics for a two-dimensional Schrödinger operator. Zbl 0910.35086
Birman, Mikhail Sh.; Laptev, Ari
1
1997
The negative discrete spectrum of a two-dimensional Schrödinger operator. Zbl 0864.35080
Birman, M. Sh.; Laptev, A.
24
1996
Szegö type limit theorems. Zbl 0878.47020
Laptev, A.; Safarov, Yu.
16
1996
A generalization of the Berezin-Lieb inequality. Zbl 0868.47016
Laptev, A.; Safarov, Yu.
6
1996
On inequalities for the bound states of Schrödinger operators. Zbl 0833.35032
Laptev, A.
1
1995
Discrete spectrum of the perturbed Dirac operator. Zbl 0822.35104
Birman, Mikhail Sh.; Laptev, Ari
12
1994
On global representations of Lagrangian distributions and solutions of hyperbolic equations. Zbl 0811.35177
Laptev, A.; Safarov, Yu.; Vassiliev, D.
6
1994
Discrete spectrum of the perturbed Dirac operator. Zbl 0858.47004
Birman, M. Sh.; Laptev, A.
4
1994
Asymptotics of the negative discrete spectrum of a class of Schrödinger operators with large coupling constant. Zbl 0795.35071
Laptev, Ari
3
1993
Error estimate in the generalized Szegö theorem. Zbl 0743.58032
Laptev, A.; Safarov, Yu.
1
1991
Spectral asymptotics of a class of Fourier integral operators. Zbl 0535.47030
Laptev, A. A.
2
1983
Spectral asymptotics of a certain class of Fourier integral operators. Zbl 0503.47044
Laptev, A. A.
5
1981
On estimates of singular numbers for a class of integral operators. Zbl 0478.47032
Laptev, A. A.
2
1981
On an estimate of the remainder term in formulas of the spectral asymptotics for one class of integral operators. Zbl 0443.47051
Laptev, A. A.
4
1977
Spectral asymptotics of a composition of pseudodifferential operators and reflections from the boundary. Zbl 0391.47035
Laptev, A. A.
1
1977
Spectral asymptotic behavior of a class of integral operators. Zbl 0322.45003
Laptev, A. A.
2
1975
all top 5

Cited by 561 Authors

49 Laptev, Ari
23 Frank, Rupert L.
18 Avkhadiev, Farit Gabidinovich
18 Safronov, Oleg
17 Dolbeault, Jean
14 Kovařík, Hynek
13 Ilyin, Alexei A.
13 Korotyaev, Evgeny L.
13 Loss, Michael
13 Nasibullin, Ramil Gaisa’evich
12 Simon, Barry
11 Krejčiřík, David
10 Cuenin, Jean-Claude
10 Esteban, Maria J.
10 Felli, Veronica
10 Solomyak, Mikhaĭl Zakharovich
9 Abatangelo, Laura
9 Weidl, Timo
8 Fanelli, Luca
8 Ruzhansky, Michael V.
8 Seiringer, Robert
8 Yolcu, Selma Yıldırım
7 Hansmann, Marcel
7 Tertikas, Achilles
7 Yolcu, Turkay
6 Ekholm, Tomas
6 Filippas, Stathis
6 Grassi, Alba
6 Harrell, Evans M. II
6 Larson, Simon
6 Mariño, Marcos
6 Suragan, Durvudkhan
6 Zelik, Sergey V.
5 Birman, Mikhail Shlëmovich
5 Denisov, Sergey A.
5 Lukic, Milivoje
5 Lundholm, Douglas
4 Barbatis, Gerassimos
4 Barseghyan, Diana
4 Bove, Antonio
4 Chen, Hua
4 Evans, William Desmond
4 Gesztesy, Fritz
4 Helffer, Bernard
4 Kachmar, Ayman
4 Karuhanga, Martin
4 Laugesen, Richard Snyder
4 Léna, Corentin
4 Lewis, Roger T.
4 Lieb, Elliott H.
4 Makarov, R. V.
4 Malamud, Mark M.
4 Molchanov, Stanislav Alekseevich
4 Naboko, Serguei N.
4 Phan Thành Nam
4 Pushnitski, Alexander B.
4 Rădulescu, Vicenţiu D.
4 Schimmer, Lukas
4 Shafigullin, Il’nar Kasyĭmovich
4 Solovej, Jan Philip
4 Vega, Luis
3 Cossetti, Lucrezia
3 Damanik, David
3 Demuth, Michael
3 Dostanić, Milutin R.
3 Exner, Pavel
3 Geisinger, Leander
3 Grubb, Gerd
3 Gu, Jie
3 Hainzl, Christian
3 Hermi, Lotfi
3 Himonas, A. Alexandrou
3 Hulko, Artem
3 Hundertmark, Dirk
3 Ibrogimov, Orif O.
3 Lam, Nguyen
3 Lewin, Mathieu
3 Lotoreichik, Vladimir
3 Lu, Guozhen
3 Melnikov, Yuri B.
3 Mughetti, Marco
3 Neidhardt, Hagen
3 Nys, Manon
3 Petronilho, Gerson
3 Portmann, Fabian
3 Robert, Didier
3 Rohleder, Jonathan
3 Safarov, Yuri G.
3 Sambou, Diomba
3 Siegl, Petr
3 Siudeja, Bartłomiej Andrzej
3 Sobolev, Alexander V.
3 Stubbe, Joachim
3 Suslina, Tat’yana Aleksandrovna
3 Takhtajan, Leon Armenovich
3 Tentarelli, Lorenzo
3 Terracini, Susanna
3 Tidblom, Jesper
3 Yafaev, Dimitri R.
3 Zinchenko, Maxim
...and 461 more Authors
all top 5

Cited in 141 Serials

53 Journal of Functional Analysis
33 Communications in Mathematical Physics
32 Journal of Mathematical Physics
31 Journal of Mathematical Analysis and Applications
18 Journal of Spectral Theory
17 Calculus of Variations and Partial Differential Equations
15 Letters in Mathematical Physics
15 Journal of Differential Equations
14 St. Petersburg Mathematical Journal
14 Annales Henri Poincaré
12 Proceedings of the American Mathematical Society
11 Advances in Mathematics
10 Integral Equations and Operator Theory
10 Bulletin of Mathematical Sciences
9 Reviews in Mathematical Physics
9 Journal of Mathematical Sciences (New York)
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 Communications in Partial Differential Equations
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Potential Analysis
7 Lobachevskii Journal of Mathematics
6 Arkiv för Matematik
6 Duke Mathematical Journal
6 Functional Analysis and its Applications
6 Transactions of the American Mathematical Society
6 Journal of the European Mathematical Society (JEMS)
6 Communications in Contemporary Mathematics
5 Annales de l’Institut Fourier
5 Mathematische Nachrichten
5 Russian Mathematics
5 Discrete and Continuous Dynamical Systems
5 Journal of High Energy Physics
4 Reports on Mathematical Physics
4 The Journal of Geometric Analysis
4 Russian Journal of Mathematical Physics
4 Mathematical Physics, Analysis and Geometry
4 Journal of Physics A: Mathematical and Theoretical
4 Ufimskiĭ Matematicheskiĭ Zhurnal
4 Analysis and Mathematical Physics
3 Archive for Rational Mechanics and Analysis
3 Journal d’Analyse Mathématique
3 Nonlinearity
3 Russian Mathematical Surveys
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Inventiones Mathematicae
3 Journal of Approximation Theory
3 Acta Applicandae Mathematicae
3 SIAM Journal on Mathematical Analysis
3 Sbornik: Mathematics
3 Doklady Mathematics
3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
3 Journal of Inequalities and Applications
3 Advanced Nonlinear Studies
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Complex Analysis and Operator Theory
2 Journal of Statistical Physics
2 Mathematical Notes
2 Archiv der Mathematik
2 Journal of Computational and Applied Mathematics
2 Journal of Soviet Mathematics
2 Mathematica Scandinavica
2 Siberian Mathematical Journal
2 Chinese Annals of Mathematics. Series B
2 Constructive Approximation
2 Journal of Scientific Computing
2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
2 Bulletin des Sciences Mathématiques
2 Journal of Fixed Point Theory and Applications
2 Banach Journal of Mathematical Analysis
1 Applicable Analysis
1 Communications on Pure and Applied Mathematics
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Mathematical Biology
1 Mathematics of Computation
1 Acta Mathematica
1 Canadian Journal of Mathematics
1 Collectanea Mathematica
1 Czechoslovak Mathematical Journal
1 Geometriae Dedicata
1 Illinois Journal of Mathematics
1 Publications Mathématiques
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Journal für die Reine und Angewandte Mathematik
1 Le Matematiche
1 Mathematische Annalen
1 Mathematische Zeitschrift
1 Memoirs of the American Mathematical Society
1 Numerische Mathematik
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Annals of Global Analysis and Geometry
1 Physica D
1 Journal of Complexity
1 Journal of the American Mathematical Society
1 Asymptotic Analysis
1 MCSS. Mathematics of Control, Signals, and Systems
1 Geometric and Functional Analysis. GAFA
1 Linear Algebra and its Applications
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
...and 41 more Serials
all top 5

Cited in 45 Fields

362 Partial differential equations (35-XX)
180 Operator theory (47-XX)
180 Quantum theory (81-XX)
76 Real functions (26-XX)
60 Ordinary differential equations (34-XX)
49 Functional analysis (46-XX)
44 Global analysis, analysis on manifolds (58-XX)
26 Difference and functional equations (39-XX)
22 Statistical mechanics, structure of matter (82-XX)
19 Calculus of variations and optimal control; optimization (49-XX)
18 Harmonic analysis on Euclidean spaces (42-XX)
12 Special functions (33-XX)
11 Differential geometry (53-XX)
11 Optics, electromagnetic theory (78-XX)
10 Dynamical systems and ergodic theory (37-XX)
10 Probability theory and stochastic processes (60-XX)
10 Numerical analysis (65-XX)
9 Algebraic geometry (14-XX)
9 Fluid mechanics (76-XX)
9 Relativity and gravitational theory (83-XX)
7 Functions of a complex variable (30-XX)
5 History and biography (01-XX)
5 Combinatorics (05-XX)
5 Topological groups, Lie groups (22-XX)
5 Mechanics of deformable solids (74-XX)
4 Potential theory (31-XX)
4 Abstract harmonic analysis (43-XX)
4 Integral transforms, operational calculus (44-XX)
4 Integral equations (45-XX)
3 Statistics (62-XX)
3 Mechanics of particles and systems (70-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Group theory and generalizations (20-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Approximations and expansions (41-XX)
2 Biology and other natural sciences (92-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 Number theory (11-XX)
1 \(K\)-theory (19-XX)
1 Measure and integration (28-XX)
1 Convex and discrete geometry (52-XX)
1 Manifolds and cell complexes (57-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year

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