Linear and Multilinear Algebra, ISSN 0308-1087, 03/2018, Volume 66, Issue 3, pp. 435 - 446

We present and compare three constructive methods for realizing nonreal spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We...

spectral theory | inverse eigenvalue problem | Nonnegative matrices | 58C40 | 47A75 | 15A18 | 15A29 | Eigen values | Realizability

spectral theory | inverse eigenvalue problem | Nonnegative matrices | 58C40 | 47A75 | 15A18 | 15A29 | Eigen values | Realizability

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 2015, Volume 81, Issue 4, pp. 455 - 482

Journal Article

Advances in Nonlinear Analysis, ISSN 2191-9496, 08/2017, Volume 8, Issue 1, pp. 707 - 714

We construct an open set on which an eigenvalue problem for the -Laplacian has no isolated first eigenvalue and the spectrum is not discrete. The same example...

Lusternik–Schnirelmann theory | 58E05 | 47A75 | 35P30 | Nonlinear eigenvalue problems | p-Laplacian | Lusternik-Schnirelmann theory

Lusternik–Schnirelmann theory | 58E05 | 47A75 | 35P30 | Nonlinear eigenvalue problems | p-Laplacian | Lusternik-Schnirelmann theory

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 02/2017, Volume 38, Issue 2, pp. 267 - 278

In this work, we present a decomposition of the scattering matrix for higher-order Sturm-Liouville problems in terms of scattering matrices associated to...

47A75 | 65L15 | scattering | Sturm-Liouville operators | spectral problems | Sturm–Liouville operators | ONE-DIMENSION | INVERSE SCATTERING | NURSING | Decomposition | Numerical analysis | Matrices (mathematics) | Scattering | Approximation | Mathematical analysis | Eigenvalues | Mathematical models | Optimization

47A75 | 65L15 | scattering | Sturm-Liouville operators | spectral problems | Sturm–Liouville operators | ONE-DIMENSION | INVERSE SCATTERING | NURSING | Decomposition | Numerical analysis | Matrices (mathematics) | Scattering | Approximation | Mathematical analysis | Eigenvalues | Mathematical models | Optimization

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 12/2016, Volume 289, Issue 17-18, pp. 2133 - 2146

We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω⊂C. Conformal regular domains support the...

elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | 47A75 | conformal mappings | eigenvalue problem | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS

elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | 47A75 | conformal mappings | eigenvalue problem | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2019, Volume 91, Issue 6, pp. 1 - 15

We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex $$\ell ^{p}$$ ℓp -potentials for $$1\le p\le \infty $$ 1≤p≤∞ ....

47B36 | Analysis | Birman–Schwinger principle | Point spectrum | 34L15 | Mathematics | 47A75 | Discrete Schrödinger operator | Jacobi matrix | LOCATION | MATHEMATICS | Discrete Schrodinger operator | Birman-Schwinger principle | EIGENVALUE BOUNDS | DIRAC

47B36 | Analysis | Birman–Schwinger principle | Point spectrum | 34L15 | Mathematics | 47A75 | Discrete Schrödinger operator | Jacobi matrix | LOCATION | MATHEMATICS | Discrete Schrodinger operator | Birman-Schwinger principle | EIGENVALUE BOUNDS | DIRAC

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2016, Volume 57, Issue 2, p. 23512

We study the spectrum of the operator D ∗ D, where the operator D, introduced in Klimek et al. [e-print arXiv:1403.7263v2], is a forward derivative on the...

PHYSICS, MATHEMATICAL | Hypergeometric functions | Trees | Operators (mathematics) | Mathematics - Spectral Theory

PHYSICS, MATHEMATICAL | Hypergeometric functions | Trees | Operators (mathematics) | Mathematics - Spectral Theory

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2020, Volume 59, Issue 1, pp. 1 - 39

We study a general class of discrete p-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational...

47B80 | 35B27 | 35R60 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 60K37 | 47A75 | 80M40 | 60H25 | MATHEMATICS | MATHEMATICS, APPLIED | STOCHASTIC HOMOGENIZATION | DIFFUSION

47B80 | 35B27 | 35R60 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 60K37 | 47A75 | 80M40 | 60H25 | MATHEMATICS | MATHEMATICS, APPLIED | STOCHASTIC HOMOGENIZATION | DIFFUSION

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 11/2015, Volume 288, Issue 16, pp. 1822 - 1833

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains Ω⊂C by reducing it, using conformal transformations, to...

elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | Eigenvalue problem | 47A75 | conformal mappings | Elliptic equations | Conformal mappings | Quasidiscs | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS

elliptic equations | 35J40 | quasidiscs | 47B25 | 35P15 | Eigenvalue problem | 47A75 | conformal mappings | Elliptic equations | Conformal mappings | Quasidiscs | MATHEMATICS | EIGENVALUES | DIMENSION | OPERATORS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2016, Volume 86, Issue 4, pp. 579 - 600

Let $$\Omega $$ Ω be an open set in Euclidean space with finite Lebesgue measure $$\vert \Omega \vert $$ | Ω | . We obtain some properties of the set function...

49J45 | 49R05 | 35P15 | Analysis | First Dirichlet eigenvalue | Mathematics | 47A75 | Torsional rigidity | 35J25

49J45 | 49R05 | 35P15 | Analysis | First Dirichlet eigenvalue | Mathematics | 47A75 | Torsional rigidity | 35J25

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 07/2018, Volume 47, Issue 13, pp. 3085 - 3091

In the paper, Karhunen-Loeve expansion and Pythagorean-type distribution identities for the additive two-sided Brownian motion are derived. As the applications...

Karhunen-Loeve expansion | 47A75 | laplace transform | small deviation | Additive two-sided Brownian Motion | 60G15 | Karhunen–Loeve expansion | Brownian movements | Laplace transforms

Karhunen-Loeve expansion | 47A75 | laplace transform | small deviation | Additive two-sided Brownian Motion | 60G15 | Karhunen–Loeve expansion | Brownian movements | Laplace transforms

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 01/2018, Volume 11, Issue 1, pp. 95 - 110

In this paper, the so-called relative -capacity is introduced and investigated in a close connection to the viscosity solution of the -Laplace equation. We not...

affinization | 47A75 | 53A15 | Relative infinity capacity | Sobolev spaces | 35J70 | Sobolev space | Laplace equation | Euclidean geometry

affinization | 47A75 | 53A15 | Relative infinity capacity | Sobolev spaces | 35J70 | Sobolev space | Laplace equation | Euclidean geometry

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 02/2020, Volume 45, Issue 2, pp. 77 - 108

In this paper we prove a regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase...

shape optimization | Alt-Caffarelli | multiphase problems | Regularity of free boundaries | 47A75 | almost-minimizers | epiperimetric inequality | Dirichlet eigenvalues | Alt-Caffarelli-Friedman | the two-phase problem | 35R35 | 49Q10 | the one-phase problem | MATHEMATICS | MATHEMATICS, APPLIED | Constraints | Multiphase | Shape optimization | Eigenvalues | Dirichlet problem | Two phase | Regularity | Free boundaries

shape optimization | Alt-Caffarelli | multiphase problems | Regularity of free boundaries | 47A75 | almost-minimizers | epiperimetric inequality | Dirichlet eigenvalues | Alt-Caffarelli-Friedman | the two-phase problem | 35R35 | 49Q10 | the one-phase problem | MATHEMATICS | MATHEMATICS, APPLIED | Constraints | Multiphase | Shape optimization | Eigenvalues | Dirichlet problem | Two phase | Regularity | Free boundaries

Journal Article

Quaestiones Mathematicae, ISSN 1607-3606, 10/2019, Volume 42, Issue 9, pp. 1185 - 1197

The eigenvalues of a class of Sturm-Liouville problems with distribution potentials and eigenparameter-dependent boundary conditions on bounded time scales are...

Primary 34B05 | eigenvalues | Secondary 47A75 | time scales | 34B40 | 34N99 | eigenparameter-dependent boundary conditions | Sturm-Liouville problems | distribution potentials

Primary 34B05 | eigenvalues | Secondary 47A75 | time scales | 34B40 | 34N99 | eigenparameter-dependent boundary conditions | Sturm-Liouville problems | distribution potentials

Journal Article

Advanced Nonlinear Studies, ISSN 1536-1365, 11/2016, Volume 16, Issue 4, pp. 689 - 697

Let Omega be a Lipschitz bounded domain of R-N, N >= 2. The fractional Cheeger constant h(s) (Omega), 0 < s < 1, is defined by h(s) (Omega) = (E subset of...

Fractional Torsion Functions | Fractional p-Laplacian | Fractional Cheeger Problem | MATHEMATICS | MATHEMATICS, APPLIED

Fractional Torsion Functions | Fractional p-Laplacian | Fractional Cheeger Problem | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

16.
Full Text
Covering numbers of isotropic reproducing kernels on compact two‐point homogeneous spaces

Mathematische Nachrichten, ISSN 0025-584X, 11/2017, Volume 290, Issue 16, pp. 2444 - 2458

In this paper we present upper and lower estimates for the covering numbers of the unit ball of a reproducing kernel Hilbert space associated to a continuous...

Covering numbers | 41A99 | 33C55 | isotropic kernels | 42A82 | eigenvalue decay | 47A75 | 22F30 | compact two‐point homogeneous spaces | positive cubature formula | compact two-point homogeneous spaces

Covering numbers | 41A99 | 33C55 | isotropic kernels | 42A82 | eigenvalue decay | 47A75 | 22F30 | compact two‐point homogeneous spaces | positive cubature formula | compact two-point homogeneous spaces

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 10/2017, Volume 23, Issue 10, pp. 1652 - 1669

In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving...

variational methods | 34B15 | 35B38 | 65Q10 | critical point theory | Discrete nonlinear boundary value problem | non trivial solution | 47A75 | MATHEMATICS, APPLIED | MULTIPLICITY | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | NONTRIVIAL SOLUTIONS | NEUMANN PROBLEMS | DISCRETE | ELLIPTIC-EQUATIONS | Dirichlet problem | Boundary conditions | Laplace transforms | Functionals | Anisotropy

variational methods | 34B15 | 35B38 | 65Q10 | critical point theory | Discrete nonlinear boundary value problem | non trivial solution | 47A75 | MATHEMATICS, APPLIED | MULTIPLICITY | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | NONTRIVIAL SOLUTIONS | NEUMANN PROBLEMS | DISCRETE | ELLIPTIC-EQUATIONS | Dirichlet problem | Boundary conditions | Laplace transforms | Functionals | Anisotropy

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2019, Volume 29, Issue 4, pp. 3124 - 3134

In this paper, we establish a kind of splitting theorem for the eigenvalues of a specific family of operators on the base of a warped product. As a...

Primary 47A75 | 47A55 | Mathematics | G-manifolds | Warped products | Laplacian | Abstract Harmonic Analysis | Fourier Analysis | Secondary 35P05 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Eigenvalues | Differential Geometry | Dynamical Systems and Ergodic Theory

Primary 47A75 | 47A55 | Mathematics | G-manifolds | Warped products | Laplacian | Abstract Harmonic Analysis | Fourier Analysis | Secondary 35P05 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Eigenvalues | Differential Geometry | Dynamical Systems and Ergodic Theory

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2013, Volume 103, Issue 12, pp. 1377 - 1388

We investigate the existence of the meromorphic extension of the spectral zeta function of a Laplacian on self-similar fractals using the results of Kigami and...

Theoretical, Mathematical and Computational Physics | spectral zeta function | 28A80 | heat kernel estimates | Secondary 30D30 | 31E05 | 47A75 | 35P20 | Statistical Physics, Dynamical Systems and Complexity | meromorphic | Physics | Laplacian | Geometry | self-similar fractals | Primary 81Q35 | Group Theory and Generalizations | 81Q10 | 60J25 | 60J35 | BROWNIAN-MOTION | PHYSICS, MATHEMATICAL | UNIQUENESS | LAPLACIANS | ITERATIONS | RESISTANCE | ASYMPTOTICS | OPERATORS | Computer science | Analysis

Theoretical, Mathematical and Computational Physics | spectral zeta function | 28A80 | heat kernel estimates | Secondary 30D30 | 31E05 | 47A75 | 35P20 | Statistical Physics, Dynamical Systems and Complexity | meromorphic | Physics | Laplacian | Geometry | self-similar fractals | Primary 81Q35 | Group Theory and Generalizations | 81Q10 | 60J25 | 60J35 | BROWNIAN-MOTION | PHYSICS, MATHEMATICAL | UNIQUENESS | LAPLACIANS | ITERATIONS | RESISTANCE | ASYMPTOTICS | OPERATORS | Computer science | Analysis

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 2167 - 2181

As a corollary we obtain lower bounds for the individual eigenvalues \lambda _k, which for a certain range of k improves the Li-Yau inequality for convex...

Berezin–Li–Yau inequality | Semi-classical estimates | Dirichlet-Laplace operator | semi-classical estimates | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequality | DIRICHLET | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Berezin–Li–Yau inequality | Semi-classical estimates | Dirichlet-Laplace operator | semi-classical estimates | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | BOUNDS | Berezin-Li-Yau inequality | DIRICHLET | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis

Journal Article

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