Výsledky vyhledávání - Completeness of eigenfunctions and eigenfunction expansions in context of PDEs

Spectral theory of the invariant Laplacian on the disk and the sphere – a complex analysis approach: Spectral theory of the invariant Laplacian on the disk and the sphere -- a complex analysis approach

Autoři: Michael Heins Annika Moucha Oliver Roth

Zdroj: Canadian Journal of Mathematics. 77:940-974

Témata: Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Möbius invariant subspaces of eigenspaces, Mathematics - Complex Variables, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Laplacian on the complement of the complexified unit circle, FOS: Physical sciences, Special domains (Reinhardt, Hartogs, circular, tube, etc.) in \(\mathbb{C}^n\) and complex manifolds, Mathematical Physics (math-ph), holomorphic eigenfunctions, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, Primary 30F45, 30H50, 35P10, Secondary 30B40, 53A55, Complex Variables (math.CV), Mathematical Physics

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2312.12900
https://zbmath.org/8034341
https://doi.org/10.4153/s0008414x2400021x

Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion: Two-component eigenfunction expansion for open systems described by the wave equation. I: Completeness of expansion

Autoři: K. Young S S Tong P T Leung

Zdroj: Journal of Physics A: Mathematical and General. 30:2139-2151

Témata: non-Hermitian, non-conservative systems, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 0103 physical sciences, Quantum equilibrium statistical mechanics (general), spatial discontinuities, 01 natural sciences, quasinormal modes

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Přístupová URL adresa: https://zbmath.org/1299713
https://doi.org/10.1088/0305-4470/30/6/034
http://iopscience.iop.org/article/10.1088/0305-4470/30/6/034/pdf
http://ui.adsabs.harvard.edu/abs/1997JPhA...30.2139L/abstract
https://iopscience.iop.org/article/10.1088/0305-4470/30/6/034/meta
http://iopscience.iop.org/article/10.1088/0305-4470/30/6/034/meta
https://iopscience.iop.org/article/10.1088/0305-4470/30/6/034/pdf

Asymptotic expansions for eigenvalues and eigenfunctions of elliptic boundary-value problems with rapidly oscillating coefficients

Autoři: Teplinsky, A.Yu.

Témata: Perturbations in context of PDEs, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, \(S\)-homogenization, elliptic operator, boundary layer, Homogenization in context of PDEs, PDEs in media with periodic structure

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1641376
http://dspace.nbuv.gov.ua/handle/123456789/169278

On Eigenfunction Expansions Associated with the Schrodinger Operator with a Singular Potential: On eigenfunction expansions associated with the Schrödinger operator with a singular potential

Autoři: Yu. E. Faiziev Ravshan Ashurov

Zdroj: Differential Equations. 41:254-263

Témata: Schrödinger operator, Riesz mean, Schrödinger operator, Schrödinger equation, Asymptotic distributions of eigenvalues in context of PDEs, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, eigenfunction expansion, Stummel condition, 0101 mathematics, 01 natural sciences, Selfadjoint operator theory in quantum theory, including spectral analysis

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Přístupová URL adresa: https://zbmath.org/2214142
https://doi.org/10.1007/s10625-005-0156-8
https://link.springer.com/article/10.1007/s10625-005-0156-8

On the Completeness of Eigenfunctions of a Nonlocal Gellerstedt Boundary Value Problem: On the completeness of eigenfunctions of a nonlocal Gellerstedt boundary value problem

Autoři: T. E. Moiseev

Zdroj: Differential Equations. 39:1653-1656

Témata: PDEs of mixed type, Asymptotic distributions of eigenvalues in context of PDEs, completeness, regular solution, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, hyperbolic part of the domain, Lavrent'ev-Bitsadze equation, eigenvalues, eigenvectors, uniqueness, 0101 mathematics, elliptic part of the domain, 01 natural sciences

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Přístupová URL adresa: https://link.springer.com/article/10.1023/B%3ADIEQ.0000019361.66675.55
https://link.springer.com/content/pdf/10.1023/B:DIEQ.0000019361.66675.55.pdf

Eigenfunction Expansion for the Three-Dimensional Dirac Operator: Eigenfunction expansion for the three-dimensional Dirac operator

Autoři: Miklós Horváth

Zdroj: Journal of Differential Equations. 160:139-174

Témata: 0301 basic medicine, 03 medical and health sciences, Dirac operator, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, PDEs in connection with relativity and gravitational theory, 0101 mathematics, convergence of spectral expansion, 01 natural sciences, Analysis, PDEs in connection with quantum mechanics, Selfadjoint operator theory in quantum theory, including spectral analysis

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Přístupová URL adresa: http://www.sciencedirect.com/science/article/pii/S0022039699936641
https://core.ac.uk/display/81183245
http://ui.adsabs.harvard.edu/abs/2000JDE...160..139H/abstract
https://www.sciencedirect.com/science/article/pii/S0022039699936641

Eigenfunction expansions and the pinsky phenomenon on compact manifolds: Eigenfunction expansions and the Pinsky phenomenon on compact manifolds

Autoři: Taylor, Michael

Zdroj: The Journal of Fourier Analysis and Applications. 7:507-522

Témata: 510.mathematics, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Spectral problems, spectral geometry, scattering theory on manifolds, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Wave equation, 0101 mathematics, 01 natural sciences, Article, Fourier integral operators applied to PDEs

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Přístupová URL adresa: https://link.springer.com/article/10.1007/BF02511223
https://link.springer.com/content/pdf/10.1007/BF02511223.pdf

An Eigenfunction Expansion for the Schrödinger Equation with Arbitrary Non-Central Potentials: An eigenfunction expansion for the Schrödinger equation with arbitrary non-central potentials

Autoři: İnci M. Erhan Hasan Taşeli Ömür Uğur

Zdroj: Journal of Mathematical Chemistry. 32:323-338

Témata: eigenvalue problems, cylindrical polar coordinates, complete set of Chebyshev polynomials, two-dimensional Schrödinger equation, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, eigenfunction expansion, 0103 physical sciences, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, non-central potential, 01 natural sciences

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1953663
https://doi.org/10.1023/a:1022949421571
https://avesis.metu.edu.tr/yayin/f3a71ba9-cad3-4a27-8a38-b6dabaefac16/an-eigenfunction-expansion-for-the-schrodinger-equation-with-arbitrary-non-central-potentials
https://link.springer.com/article/10.1023/A:1022949421571
https://link.springer.com/content/pdf/10.1023/A:1022949421571.pdf

Green functions and eigenfunction expansions for the square of the Laplace–Beltrami operator on plane domains: Green functions and eigenfunction expansions for the square of the Laplace-Beltrami operator on plane domains

Autoři: Jaak Peetre Miroslaw Englis

Zdroj: Annali di Matematica Pura ed Applicata. 181:463-500

Témata: Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Fuchsian group, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, eigenfunction expansion, 02 engineering and technology, biharmonic operator, 01 natural sciences, Poincaré metric, Green function, Laplace-Beltrami operator, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Other functions coming from differential, difference and integral equations, Boundary value problems on manifolds

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Přístupová URL adresa: https://zbmath.org/2216114
https://doi.org/10.1007/s10231-002-0051-3
https://portal.research.lu.se/sv/publications/green-functions-and-eigenfunction-expansions-for-the-square-of-th
https://lup.lub.lu.se/search/publication/126cb44d-82ba-4422-91a0-5dc4dd7ca546
https://link.springer.com/article/10.1007%2Fs10231-002-0051-3
https://link.springer.com/content/pdf/10.1007/s10231-002-0051-3.pdf
https://www.lunduniversity.lu.se/lup/publication/126cb44d-82ba-4422-91a0-5dc4dd7ca546

Sequential eigenfunction expansion for a problem in combustion theory

Autoři: K. K. Tam M. Al-Refai

Zdroj: The ANZIAM Journal. 45:35-48

Témata: sub-critical, Reaction-diffusion equations, super-critical, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Combustion, semilinear parabolic equation, ordinary differential equation, 0101 mathematics, steady-state solutions, 01 natural sciences

Popis souboru: application/xml

Přístupová URL adresa: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/99B41769E333F7FD3266908BB1EB351E/S1446181100013146a.pdf/div-class-title-sequential-eigenfunction-expansion-for-a-problem-in-combustion-theory-div.pdf
https://zbmath.org/2064246
https://doi.org/10.1017/s1446181100013146
https://dialnet.unirioja.es/servlet/articulo?codigo=657068

Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation

Autoři: Vladimir V. Varlamov

Zdroj: Discrete & Continuous Dynamical Systems - A. 7:675-702

Témata: semilinear dissipative equations, Asymptotic behavior of solutions to PDEs, Initial-boundary value problems for second-order parabolic equations, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Nonlinear parabolic equations, uniqueness, higher-order long-time asymptotics, 0101 mathematics, PDEs in connection with fluid mechanics, damped Boussinesq equation, mild global-in-time solutions, 01 natural sciences

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Přístupová URL adresa: https://www.aimsciences.org/article/doi/10.3934/dcds.2001.7.675

Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure: Two-component eigenfunction expansion for open systems described by the wave equation. II: Linear space structure

Autoři: P T Leung K. Young S S Tong

Zdroj: Journal of Physics A: Mathematical and General. 30:2153-2162

Témata: mutually orthogonal, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 0103 physical sciences, time-evolution operator, Quantum equilibrium statistical mechanics (general), time-independence perturbation theory, 01 natural sciences, quasinormal modes

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Přístupová URL adresa: https://zbmath.org/1299714
https://doi.org/10.1088/0305-4470/30/6/035
http://iopscience.iop.org/article/10.1088/0305-4470/30/6/035/meta
https://ui.adsabs.harvard.edu/abs/1997JPhA...30.2153L/abstract
https://iopscience.iop.org/article/10.1088/0305-4470/30/6/035
https://iopscience.iop.org/article/10.1088/0305-4470/30/6/035/pdf

An Uncertainty Principle for Eigenfunction Expansions: An uncertainty principle for eigenfunction expansions.

Autoři: V. Pati S. Thangavelu M. Sundari a další

Zdroj: Journal of Fourier Analysis and Applications. 2:427-433

Témata: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), General theory of partial differential operators, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Spectral problems, spectral geometry, scattering theory on manifolds, 0101 mathematics, 01 natural sciences

Popis souboru: application/xml

Přístupová URL adresa: https://link.springer.com/article/10.1007%2Fs00041-001-4036-2
http://repository.ias.ac.in/108970/
https://eudml.org/doc/59489

The Rayleigh hydrodynamical problem: a theorem on eigenfunction expansion and the stability of plane-parallel flows: The Rayleigh hydrodynamical problem: A theorem on eigenfunction expansion and the stability of plane-parallel flows

Autoři: S. A. Stepin

Zdroj: Izvestiya: Mathematics. 60:1293-1316

Témata: singular non-selfadjoint boundary value problem, Friedrichs model, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, operator formulation, method of contour integration, stationary theory of scattering, Green's function, 0101 mathematics, 01 natural sciences, spectral analysis, Parallel shear flows in hydrodynamic stability

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1094678
https://doi.org/10.1070/im1996v060n06abeh000100
http://ui.adsabs.harvard.edu/abs/1996IzMat..60.1293S/abstract
https://iopscience.iop.org/article/10.1070/IM1996v060n06ABEH000100/meta

Asymptotic expansions of eigenvalues and eigenfunctions for elliptic boundary-value problems with rapidly oscillating coefficients in a perforated cube

Autoři: T. A. Melnik

Zdroj: Journal of Mathematical Sciences. 75:1646-1671

Témata: Boundary value problems for second-order elliptic equations, complete asymptotic expansions, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, \(\varepsilon\)-periodic coefficients, 0101 mathematics, Homogenization in context of PDEs, PDEs in media with periodic structure, 01 natural sciences, Asymptotic expansions of solutions to PDEs

Popis souboru: application/xml

Přístupová URL adresa: https://link.springer.com/article/10.1007%2FBF02368668

Continuous spectrum eigenfunction expansions and the Cauchy problem in L 1: Continuous spectrum eigenfunction expansions and the Cauchy problem in \(L_ 1\)

Autoři: David E. Edmunds Robert M. Kauffman

Zdroj: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences. 441:407-422

Témata: Cauchy problem, continuous spectrum eigenfunction expansion, kernel function, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 0101 mathematics, (Generalized) eigenfunction expansions of linear operators, rigged Hilbert spaces, 01 natural sciences, Higher-order parabolic equations, approximation of the solution by finite sums

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/490474
https://doi.org/10.1098/rspa.1993.0070
http://rspa.royalsocietypublishing.org/content/441/1912/407
https://ui.adsabs.harvard.edu/abs/1993RSPSA.441..407E/abstract

Notes to my paper 'on the convergence of eigenfunction expansions in the norm of Soboleff spaces': Notes to my paper ``On the convergence of eigenfunction expansion in the norm of Sobolev spaces''

Autoři: I. Joó

Zdroj: Acta Mathematica Hungarica. 62:285-291

Témata: Schrödinger operator, Schrödinger equation, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences

Popis souboru: application/xml

Přístupová URL adresa: https://link.springer.com/article/10.1007/BF01874649
https://link.springer.com/10.1007/BF01874649

Calculations on nonlinear dielectric slab waveguides by the iterative eigenfunction expansion method

Autoři: A.D. Klemm Y.-J. Gong

Zdroj: Applied Mathematical Modelling. 16:605-609

Témata: iterative eigenfunction expansion method, Applied Mathematics, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, finite element method, nonlinear waves, 02 engineering and technology, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Antennas, waveguides in optics and electromagnetic theory, nonlinear optical waveguides, 01 natural sciences, Applications to the sciences, Modelling and Simulation, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, PDEs in connection with optics and electromagnetic theory

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/167009
https://doi.org/10.1016/0307-904x(92)90036-3
https://www.sciencedirect.com/science/article/pii/0307904X92900363
https://www.sciencedirect.com/science/article/abs/pii/0307904X92900363

Local uniform convergence of the eigenfunction expansion associated with the Laplace operator. I

Autoři: M. Horváth

Zdroj: Acta Mathematica Hungarica. 64:1-25

Témata: Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Bessel-Macdonald kernel, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 0103 physical sciences, Liouville class, Bessel and Airy functions, cylinder functions, \({}_0F_1\), 0101 mathematics, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), 01 natural sciences, Riesz basis

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/556321
https://doi.org/10.1007/bf01874116
https://link.springer.com/article/10.1007/BF01874116
https://link.springer.com/content/pdf/10.1007/BF01874116.pdf

The eigenfunction expansion method in dynamic electroelasticity problems

Autoři: O. Yu. Zharii

Zdroj: Journal of Applied Mathematics and Mechanics. 54:88-93

Témata: piezoelectrics, Elastic materials, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, 02 engineering and technology, solution of Laplace's equation, nonstationary dynamic problems, piezoceramic rod, anisotropic medium, 0203 mechanical engineering, Electromagnetic effects in solid mechanics, orthogonality property, electric potential, series in non-orthogonal eigenfunctions, instantaneous electrical loading, Dynamical problems in solid mechanics, 0210 nano-technology, singularities

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/25537
https://doi.org/10.1016/0021-8928(90)90093-p
https://www.sciencedirect.com/science/article/abs/pii/002189289090093P
https://ui.adsabs.harvard.edu/abs/1990JApMM..54...88Z/abstract
https://www.sciencedirect.com/science/article/pii/002189289090093P#!