Partial differential equations, spectral theory, and mathematical physics. The Ari Laptev anniversary volume. (English) Zbl 1465.35005

EMS Series of Congress Reports. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-007-5/hbk; 978-3-98547-507-0/ebook). xii, 481 p. (2021).

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Publisher’s description: This volume is dedicated to Ari Laptev on the occasion of his 70th birthday. It collects contributions by his numerous colleagues sharing with him research interests in analysis and spectral theory.
In brief, the topics covered include Friedrichs, Hardy, and Lieb-Thirring inequalities, eigenvalue bounds and asymptotics, Feshbach-Schur maps and perturbation theory, scattering theory and orthogonal polynomials, stability of matter, electron density estimates, Bose-Einstein condensation, Wehrl-type entropy inequalities, Bogoliubov theory, wave packet evolution, heat kernel estimates, homogenization, d-bar problems, Brezis-Nirenberg problems, the nonlinear Schrödinger equation in magnetic fields, classical discriminants, and the two-dimensional Euler-Bardina equations. In addition, Ari’s multifaceted service to the mathematical community is also touched upon.
Altogether the volume presents a collection of research articles which will be of interest to any active scientist working in one of the above mentioned fields.
The articles of this volume will be reviewed individually.
Indexed articles:
Benguria, Rafael D.; Benguria, Soledad, A non-existence result for a generalized radial Brezis-Nirenberg problem, 1-15 [Zbl 1480.35204]
Cianchi, Andrea; Maz’ya, Vladimir G., Friedrichs-type inequalities in arbitrary domains, 17-38 [Zbl 1489.46040]
Davies, E. Brian, Ari Laptev and the journal of spectral theory, 39-40 [Zbl 1479.35005]
Dolbeault, Jean; Esteban, Maria J.; Loss, Michael, Critical magnetic field for 2D magnetic Dirac-Coulomb operators and Hardy inequalities, 41-63 [Zbl 1480.81044]
Dusson, Geneviève; Sigal, Israel Michael; Stamm, Benjamin, The Feshbach-Schur map and perturbation theory, 65-88 [Zbl 07438887]
Kammerer, Clotilde Fermanian; Lasser, Caroline; Robert, Didier, Adiabatic and non-adiabatic evolution of wave packets and applications to initial value representations, 89-113 [Zbl 1479.35975]
Fournais, Søren, Length scales for BEC in the dilute Bose gas, 115-133 [Zbl 1480.81133]
Frank, Rupert L.; Gontier, David; Lewin, Mathieu, The periodic Lieb-Thirring inequality, 135-154 [Zbl 1480.81045]
Frank, Rupert L.; Larson, Simon, Semiclassical asymptotics for a class of singular Schrödinger operators, 155-176 [Zbl 1479.35585]
Grebenkov, Denis S.; Helffer, Bernard; Moutal, Nicolas, On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains, 177-196 [Zbl 1515.47030]
Hundertmark, Dirk; Kunstmann, Peer Christian; Ried, Tobias; Vugalter, Semjon, Counting bound states with maximal Fourier multipliers, 197-207 [Zbl 1479.35583]
Ilyin, Alexei A.; Zelik, Sergey, Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations, 209-229 [Zbl 1479.35101]
Ivrii, Victor, Upper estimates for the electronic density in heavy atoms and molecules, 231-245 [Zbl 1479.35586]
Kieffer, Thomas F.; Loss, Michael, Non-linear Schrödinger equation in a uniform magnetic field, 247-265 [Zbl 1479.35797]
Klein, Christian; Sjöstrand, Johannes; Stoilov, Nikola, Large \(|k|\) behavior of d-bar problems for domains with a smooth boundary, 267-275 [Zbl 1480.81056]
Kovařík, Hynek, Heat kernel estimates for two-dimensional relativistic Hamiltonians with magnetic field, 277-288 [Zbl 1515.47059]
Kupin, Stanislas; Naboko, Sergey, A version of Watson lemma for Laplace integrals and some applications, 289-300 [Zbl 1510.44001]
Lieb, Elliott H.; Solovej, Jan Philip, Wehrl-type coherent state entropy inequalities for \(\mathrm{SU}(1,1)\) and its \(AX+B\) subgroup, 301-314 [Zbl 1480.81064]
Mikhalkin, Evgeny; Stepanenko, Vitaly; Tsikh, Avgust, Blow-ups for the Horn-Kapranov parametrization of the classical discriminant, 315-329 [Zbl 1478.32040]
Rozenblum, Grigori; Shargorodsky, Eugene, Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case, 331-354 [Zbl 1515.47024]
Safronov, Oleg, Relations between two parts of the spectrum of a Schrödinger operator and other remarks on the absolute continuity of the spectrum in a typical case, 355-365 [Zbl 1480.81049]
Schlein, Benjamin, Bogoliubov theory for many-body quantum systems, 367-388 [Zbl 1496.35335]
Siedentop, Heinz, A statistical theory of heavy atoms: asymptotic behavior of the energy and stability of matter, 389-403 [Zbl 1480.81130]
Suslina, Tatiana A., Homogenization of the higher-order Schrödinger-type equations with periodic coefficients, 405-426 [Zbl 1479.35064]
Takhtajan, Leon A., Trace formulas for the modified Mathieu equation, 427-443 [Zbl 1515.47060]
Tretter, Christiane, Eigenvalue accumulation and bounds for non-selfadjoint matrix differential operators related to NLS, 445-456 [Zbl 1478.35157]
Yafaev, Dmitri, Scattering theory for Laguerre operators, 457-478 [Zbl 1484.33018]


35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
47-06 Proceedings, conferences, collections, etc. pertaining to operator theory
81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
00B15 Collections of articles of miscellaneous specific interest
00B30 Festschriften

Biographic References:

Laptev, Ari
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