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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2019, Volume 473, Issue 2, pp. 1253 - 1269
We prove Berezin–Li–Yau inequalities for the Dirichlet and Neumann eigenvalues on domains on the sphere Sd−1. A sharp explicit bound for the sums of the... 
Berezin–Li–Yau inequalities | Riesz means | Estimation of eigenvalues | Spherical harmonics | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequalities | SUMS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 03/2020, Volume 22, Issue 2, p. 1950008
We study bounds on the Riesz means of the mixed Steklov–Neumann and Steklov–Dirichlet eigenvalue problem on a bounded domain Ω in ℝ n . The Steklov–Neumann... 
Riesz mean | MATHEMATICS | MATHEMATICS, APPLIED | Dirichlet-to-Neumann operator | Sloshing problem | mixed Steklov eigenvalue problem
Journal Article
Communications in mathematical physics, ISSN 1432-0916, 2019, Volume 375, Issue 3, pp. 2071 - 2087
This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrodinger operator involving an Aharonov-Bohm magnetic... 
BREAKING | CAFFARELLI-KOHN-NIRENBERG | EQUATIONS | EXTREMAL-FUNCTIONS | SHARP CONSTANTS | PHYSICS, MATHEMATICAL | SOBOLEV | Mathematical Physics | Analysis of PDEs | Mathematics
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2016, Volume 207, Issue 10, pp. 1410 - 1434
Journal Article
Journal of mathematical physics, ISSN 1089-7658, 2017, Volume 58, Issue 1, p. 012105
...JOURNAL OF MATHEMATICAL PHYSICS 58, 012105 (2017) Perturbations of embedded eigenvalues for a magnetic Schrödinger operator on a cylinder Ari Laptev 1... 
PSEUDO-LAPLACIANS | POTENTIALS | SPECTRUM | PHYSICS, MATHEMATICAL | BILAPLACIAN | Operators (mathematics) | Eigenvalues | Decay rate | Mathematical analysis | Eigen values | Cylinders | Fysik | Physical Sciences | Naturvetenskap | Natural Sciences
Journal Article
Bulletin of mathematical sciences, ISSN 1664-3615, 2018, Volume 8, Issue 3, pp. 453 - 475
... lattices Evgeny Korotyaev 1 · Ari Laptev 2 Received: 4 January 2018 / Accepted: 22 January 2018 / Published online: 13 March 2018 © The Author(s) 2018. This article... 
Complex eigenvalues | Scattering | 34B24, 47E05 | Trace formula | Hardy spaces | 34A55 | Mathematics, general | Mathematics | Lattice | DISCRETE SCHRODINGER | MATHEMATICS | INEQUALITIES | EIGENVALUE BOUNDS
Journal Article
Communications in mathematical physics, ISSN 1432-0916, 2009, Volume 292, Issue 1, pp. 29 - 54
We discuss properties of eigenvalues of non-self-adjoint Schrodinger operators with complex-valued potential V. Among our results are estimates of the sum of... 
PHYSICS, MATHEMATICAL | BOUNDS | INEQUALITIES
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 5/2018, Volume 19, Issue 5, pp. 1439 - 1463
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 06/2015, Volume 268, Issue 11, pp. 3278 - 3289
In this paper we obtain some sharp Hardy inequalities with weight functions that may admit singularities on the unit sphere. In order to prove the main results... 
Hardy inequalities | Laplace–Beltrami operators | Secondary | Laplace-Beltrami operators | Primary | MATHEMATICS | OPERATOR
Journal Article
Analysis and Mathematical Physics, ISSN 1664-2368, 9/2019, Volume 9, Issue 3, pp. 1535 - 1546
We study the spectrum of a system of second order differential operator $$D_m$$ D m perturbed by a non-selfadjoint matrix valued potential V. We prove that... 
Mathematical Methods in Physics | Analysis | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDS | SCHRODINGER-OPERATORS
Journal Article
Journal of the London Mathematical Society, ISSN 1469-7750, 2016, Volume 94, Issue 2, pp. 377 - 390
We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the... 
MATHEMATICS | INEQUALITIES | VALUED POTENTIALS | BOUNDS | DIFFERENTIAL-OPERATORS
Journal Article
MATHEMATICA SCANDINAVICA, ISSN 0025-5521, 2019, Volume 125, Issue 1-2, pp. 239 - 269
In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian type magnetic field. Moreover, we obtain a... 
MATHEMATICS | RELLICH-TYPE INEQUALITIES | CAFFARELLI-KOHN-NIRENBERG
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2017, Volume 11, Issue 4, pp. 895 - 926
... of the Zaremba Problem for the Circle Ari Laptev 1,2 · Anastasiya Peicheva 2 · Alexander Shlapunov 2 Received: 15 January 2016 / Accepted: 24 October 2016 / Published online... 
Robin condition | Operator Theory | Analysis | Eigenvalues | Mathematics, general | Mathematics | 30B60 | 47A10 | 35J57 | Sturm-Liouville problems | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | COMPLETENESS | Computer science
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 2/2016, Volume 26, Issue 1, pp. 288 - 305
... Geometric And Functional Analysis WEYL TYPE ASYMPTOTICS AND BOUNDS FOR THE EIGENV ALUES OF FUNCTIONAL-DIFFERENCE OPERA TORS FOR MIRROR CUR VES Ari Laptev, Lukas... 
Analysis | Mathematics
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2015, Volume 128, pp. 365 - 379
In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in... 
Hardy inequality | [formula omitted]-Laplacian | Robin boundary conditions | p-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | GEOMETRICAL VERSION | EQUATIONS | CONSTANT | DOMAINS
Journal Article
Journal of mathematical physics, ISSN 1089-7658, 2018, Volume 59, Issue 5, p. 051504
We study functional and spectral properties of perturbations of the operator −(∂s+i a)2 in L2(S1). This operator appears when considering the restriction to... 
HARDY INEQUALITIES | PHYSICS, MATHEMATICAL | SPHERE | SCHRODINGER-OPERATORS | Mathematics | Mathematical Physics | Analysis of PDEs | Physics
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2016, Volume 2016, Issue 4, pp. 1190 - 1222
In this paper, we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the... 
MATHEMATICS | BOUNDS | LIEB-THIRRING INEQUALITIES
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 3/2014, Volume 326, Issue 2, pp. 531 - 541
... Inequalities for Schrödinger Operators on Semiaxis Pavel Exner 1,2 , Ari Laptev 3 , Muhammad Usman 4 1 Doppler Institute for Mathematical Physics and Applied Mathematics... 
Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | LIEB-THIRRING INEQUALITIES | PROOF | CONSTANTS | PHYSICS, MATHEMATICAL | BOUNDS | Nuclear physics
Journal Article
Journal of Spectral Theory, ISSN 1664-039X, 2016, Volume 6, Issue 4, pp. 837 - 858
We obtain a number of Hardy type inequalities for continuous and discrete operators. 
Hardy's inequalties | Discrete Schödinger operators | MATHEMATICS | MATHEMATICS, APPLIED | discrete Schodinger operators
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 10/2014, Volume 90, Issue 2, pp. 525 - 550
Journal Article
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