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## Search Articles

Complex analysis and operator theory, ISSN 1661-8262, 08/2018, Volume 13, Issue 3, pp. 1111 - 1131

.... Simple examples show that eigenfunctions may form a complete set for a narrow strip, but completeness may be lost for a wide strip...

Eigenfunction expansion | Periodic differential operator | 47D06 | Operator Theory | Analysis | 34M03 | Mathematics, general | Mathematics | Semigroup generators | 34L10 | Hardy space | Physical Sciences | Mathematics, Applied | Science & Technology | Operators (mathematics) | Strip | Analytic functions | Mathematical analysis | Completeness | Differential equations | Hilbert space | Eigenvectors | Coefficients | Quantum theory

Eigenfunction expansion | Periodic differential operator | 47D06 | Operator Theory | Analysis | 34M03 | Mathematics, general | Mathematics | Semigroup generators | 34L10 | Hardy space | Physical Sciences | Mathematics, Applied | Science & Technology | Operators (mathematics) | Strip | Analytic functions | Mathematical analysis | Completeness | Differential equations | Hilbert space | Eigenvectors | Coefficients | Quantum theory

Journal Article

2016, Volume 679

General theory of linear operators | Other Dirichlet series and zeta functions | Completeness of eigenfunctions, eigenfunction expansions | Analytic functions | Functions of a complex variable | Partial differential equations | Spaces and algebras of analytic functions | Cyclic vectors, hypercyclic and chaotic operators | Bounded analytic functions | Spectral theory and eigenvalue problems | Operator theory | Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) | Special classes of linear operators | Bergman spaces, Fock spaces | Analytic spaces | Zeta and $L$-functions: analytic theory | Number theory

Conference Proceeding

Journal of spectral theory, ISSN 1664-039X, 2014, Volume 4, Issue 2, pp. 349 - 364

< (k + 1)pi/2k. We get asymptotic expansions for the instability indices, extending the results of [4] and [5].

Asymptotic expansions | Complex WKB method | Non-selfadjoint operators | Completeness of eigenfunctions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Asymptotic expansions | Complex WKB method | Non-selfadjoint operators | Completeness of eigenfunctions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of vibration and control, ISSN 1077-5463, 6/2013, Volume 19, Issue 8, pp. 1208 - 1215

The eigenfunction system of the Hamiltonian operator appearing in the free vibration of rectangular Kirchhoff plates with two opposite edges simply supported is studied...

completeness | Free vibration | symplectic elasticity | Hamiltonian operator | Kirchhoff plate | Mechanics | Engineering | Acoustics | Technology | Engineering, Mechanical | Science & Technology | Elasticity | Analysis | Vibration control | Boundary conditions | Vibration | Cauchy problems | Differential equations | Eigen values | Operators | Mathematical analysis | Eigenfunctions | Plates

completeness | Free vibration | symplectic elasticity | Hamiltonian operator | Kirchhoff plate | Mechanics | Engineering | Acoustics | Technology | Engineering, Mechanical | Science & Technology | Elasticity | Analysis | Vibration control | Boundary conditions | Vibration | Cauchy problems | Differential equations | Eigen values | Operators | Mathematical analysis | Eigenfunctions | Plates

Journal Article

5.
Full Text
On the eigenfunction expansions associated with semilinear Sturm–Liouville-type problems

Nonlinear analysis, ISSN 0362-546X, 2009, Volume 70, Issue 12, pp. 4123 - 4139

.... Mainly, we study problems in the interval
(
0
,
1
)
. It is shown that in this case each problem that we deal with has an infinite sequence of solutions or eigenfunctions...

Eigenfunction expansion | Semilinear Sturm–Liouville operator | Completeness of eigenfunctions | Problem in a half-line | Fourier transform | Problem in a bounded interval | Basis | Boundary value problem | Autonomous equation | Eigenvalue problem | Linear independence | Bari theorem | Riesz basis | Semilinear Sturm-Liouville operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Eigenfunction expansion | Semilinear Sturm–Liouville operator | Completeness of eigenfunctions | Problem in a half-line | Fourier transform | Problem in a bounded interval | Basis | Boundary value problem | Autonomous equation | Eigenvalue problem | Linear independence | Bari theorem | Riesz basis | Semilinear Sturm-Liouville operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 09/2015, Volume 111, Issue 3, pp. 749 - 773

In this paper, we study the boundary traces of eigenfunctions on the boundary of a smooth and bounded domain...

Physical Sciences | Mathematics | Science & Technology | Functions (mathematics) | Asymptotic properties | Mathematical analysis | Completeness | Dirichlet problem | Eigenfunctions | Boundary conditions | Boundaries

Physical Sciences | Mathematics | Science & Technology | Functions (mathematics) | Asymptotic properties | Mathematical analysis | Completeness | Dirichlet problem | Eigenfunctions | Boundary conditions | Boundaries

Journal Article

Ufa Mathematical Journal, 2017, Volume 9, Issue 1, pp. 109 - 122

Journal Article

Iranian journal of science and technology. Transaction A, Science, ISSN 1028-6276, 3/2016, Volume 40, Issue 1, pp. 1 - 8

In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm...

Transmission conditions | Engineering | Life Sciences, general | Chemistry/Food Science, general | Materials Science, general | Eigenfunction | Eigenvalue | Earth Sciences, general | Engineering, general | Physics, general | Resolvent operator | Sturm–Liouville problem | Sturm-liouville problem | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Boundary conditions | Hilbert space | Eigenvectors | Completeness | Linear operators

Transmission conditions | Engineering | Life Sciences, general | Chemistry/Food Science, general | Materials Science, general | Eigenfunction | Eigenvalue | Earth Sciences, general | Engineering, general | Physics, general | Resolvent operator | Sturm–Liouville problem | Sturm-liouville problem | Science & Technology - Other Topics | Multidisciplinary Sciences | Science & Technology | Boundary conditions | Hilbert space | Eigenvectors | Completeness | Linear operators

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2006, Volume 134, Issue 12, pp. 3487 - 3494

For p\geqslant \frac{12}{11}, the eigenfunctions of the non-linear eigenvalue problem for the p-Laplacian on the interval (0,1...

Mathematical intervals | Mathematical completeness | Differential equations | Eigenvalues | Linear transformations | Sine function | Eigenfunctions | Mathematical functions | College mathematics | Eigenfunction completeness | p-Laplacian eigenvalues | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Mathematical intervals | Mathematical completeness | Differential equations | Eigenvalues | Linear transformations | Sine function | Eigenfunctions | Mathematical functions | College mathematics | Eigenfunction completeness | p-Laplacian eigenvalues | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

IMA journal of applied mathematics, ISSN 1464-3634, 06/2007, Volume 72, Issue 3, pp. 376 - 394

.... It is demonstrated that the underlying eigenfunctions are linearly dependent and, most significantly, that an eigenfunction-expansion representation of a suitably smooth function, say f(y...

Eigenfunction expansion | Point-wise convergence | Linear dependence | Elastic plates and membranes | Acoustic wave-guide | Completeness | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Eigenfunction expansion | Point-wise convergence | Linear dependence | Elastic plates and membranes | Acoustic wave-guide | Completeness | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Computational mathematics and mathematical physics, ISSN 0965-5425, 1/2015, Volume 55, Issue 1, pp. 1 - 7

A finite-difference method is used to prove the completeness of the eigenfunctions of the Sturm-Liouville operator in conservative form...

finite-difference method | Sturm-Liouville operator | completeness of eigenfunctions | Computational Mathematics and Numerical Analysis | Mathematics | self-adjoint finite-difference schemes | Physical Sciences | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Studies | Mathematical analysis | Differential equations | Eigen values | Operators | Approximation | Completeness | Eigenfunctions | Boundary conditions | Mathematical models | Finite difference method

finite-difference method | Sturm-Liouville operator | completeness of eigenfunctions | Computational Mathematics and Numerical Analysis | Mathematics | self-adjoint finite-difference schemes | Physical Sciences | Mathematics, Applied | Physics | Physics, Mathematical | Science & Technology | Studies | Mathematical analysis | Differential equations | Eigen values | Operators | Approximation | Completeness | Eigenfunctions | Boundary conditions | Mathematical models | Finite difference method

Journal Article

Mediterranean journal of mathematics, ISSN 1660-5446, 2/2016, Volume 13, Issue 1, pp. 153 - 170

... A. We obtain asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that the eigenelements of A are complete in H.

34B27 | 47E05 | transmission conditions | spectrum | Mathematics, general | Mathematics | completeness | eigenparameter-dependent boundary conditions | asymptotics of eigenvalues and eigenfunctions | 34L10 | 34L20 | Sturm–Liouville problems | Physical Sciences | Mathematics, Applied | Science & Technology

34B27 | 47E05 | transmission conditions | spectrum | Mathematics, general | Mathematics | completeness | eigenparameter-dependent boundary conditions | asymptotics of eigenvalues and eigenfunctions | 34L10 | 34L20 | Sturm–Liouville problems | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

Resultate der Mathematik, ISSN 1422-6383, 9/2017, Volume 72, Issue 1, pp. 281 - 301

A class of polynomial pencils of ordinary differential operators with constant coefficients is considered in the article. The pencils from this class are...

eigenfunctions | 47E05 | Primary 34L10 | root functions | associated functions | system of root functions | Mathematics, general | Pencil of ordinary differential operators | Mathematics | multiple completeness | polynomial pencil of operators | Secondary 34B07 | Physical Sciences | Mathematics, Applied | Science & Technology

eigenfunctions | 47E05 | Primary 34L10 | root functions | associated functions | system of root functions | Mathematics, general | Pencil of ordinary differential operators | Mathematics | multiple completeness | polynomial pencil of operators | Secondary 34B07 | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

Russian mathematics, ISSN 1066-369X, 3/2008, Volume 52, Issue 3, pp. 45 - 57

... (we choose a bundle graph as a model). This leads to an important problem, namely, to the expansion of a given function in eigenfunctions of the corresponding Sturm-Liouville problem on a grid...

eigenfunctions | completeness of system of eigenfunctions | Mathematics, general | Mathematics | the Green function | boundary-value problem on a graph | expansion in eigenfunctions

eigenfunctions | completeness of system of eigenfunctions | Mathematics, general | Mathematics | the Green function | boundary-value problem on a graph | expansion in eigenfunctions

Journal Article

Boundary value problems, ISSN 1687-2770, 07/2018, Volume 2018, Issue 1, pp. 1 - 15

.... Operator formulation is built and asymptotic formulas for eigenvalues and eigenfunctions are given...

Ordinary Differential Equations | Analysis | Transmission condition | Completeness | Difference and Functional Equations | Approximations and Expansions | Eigenparameter dependent boundary condition | Asymptotic formulae of eigenvalue and eigenfunction | Mathematics, general | Mathematics | Sturm–Liouville problem | Partial Differential Equations | Physical Sciences | Mathematics, Applied | Science & Technology | Eigenvalues | Boundary conditions | Eigenvectors

Ordinary Differential Equations | Analysis | Transmission condition | Completeness | Difference and Functional Equations | Approximations and Expansions | Eigenparameter dependent boundary condition | Asymptotic formulae of eigenvalue and eigenfunction | Mathematics, general | Mathematics | Sturm–Liouville problem | Partial Differential Equations | Physical Sciences | Mathematics, Applied | Science & Technology | Eigenvalues | Boundary conditions | Eigenvectors

Journal Article

Chinese physics B, ISSN 1674-1056, 2011, Volume 20, Issue 12, pp. 264 - 272

The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved...

对称算子 | 算子矩阵 | 完备性定理 | 函数系统 | 弹性特征 | Hamilton | eigenfunction system | symplectic orthogonal | completeness | Operator matrix | Hamiltonian operator | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Operators | Theorems | Free vibration | Mathematical analysis | Completeness | Bending | Eigenfunctions | Mathematical models | Symmetry

对称算子 | 算子矩阵 | 完备性定理 | 函数系统 | 弹性特征 | Hamilton | eigenfunction system | symplectic orthogonal | completeness | Operator matrix | Hamiltonian operator | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Operators | Theorems | Free vibration | Mathematical analysis | Completeness | Bending | Eigenfunctions | Mathematical models | Symmetry

Journal Article

Discrete dynamics in nature and society, ISSN 1026-0226, 3/2017, Volume 2017, pp. 1 - 12

.... Moreover, the completeness of eigenfunctions is discussed.

Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Problems | Boundary conditions | Hilbert space | Researchers | Research | Formulations | Discontinuity | Operators | Dynamics | Completeness | Eigenvalues | Eigenfunctions

Mathematics, Interdisciplinary Applications | Science & Technology - Other Topics | Physical Sciences | Multidisciplinary Sciences | Mathematics | Science & Technology | Problems | Boundary conditions | Hilbert space | Researchers | Research | Formulations | Discontinuity | Operators | Dynamics | Completeness | Eigenvalues | Eigenfunctions

Journal Article

18.
Full Text
Quasi-normal-modes description of transmission properties for photonic bandgap structures

Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, 04/2009, Volume 26, Issue 4, pp. 876 - 891

We use the "quasi-normal-modes" (QNM) approach for discussing the transmission properties of double-side opened optical cavities: in particular, this approach...

FINITE | WAVE-EQUATION | COMPLETENESS | OPEN SYSTEMS | RESONANCES | 2-COMPONENT EIGENFUNCTION EXPANSION | GAP STRUCTURES | SCATTERING | PROPAGATION | OPTICAL CAVITIES | Optics | Physical Sciences | Science & Technology

FINITE | WAVE-EQUATION | COMPLETENESS | OPEN SYSTEMS | RESONANCES | 2-COMPONENT EIGENFUNCTION EXPANSION | GAP STRUCTURES | SCATTERING | PROPAGATION | OPTICAL CAVITIES | Optics | Physical Sciences | Science & Technology

Journal Article

Science in China. Series A, Mathematics, physics, astronomy, ISSN 1006-9283, 1/2009, Volume 52, Issue 1, pp. 173 - 180

The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the sufficient conditions of the completeness in the sense of Cauchy principal value...

eigenfunction system | infinite dimensional Hamiltonian operator k -compact operator | Cauchy principal value | Mathematics | 47A75 | Applications of Mathematics | completeness | eigenvalue | Eigenvalue | Infinite dimensional Hamiltonian operator k-compact operator | Eigenfunction system | Completeness | Physical Sciences | Mathematics, Applied | Science & Technology

eigenfunction system | infinite dimensional Hamiltonian operator k -compact operator | Cauchy principal value | Mathematics | 47A75 | Applications of Mathematics | completeness | eigenvalue | Eigenvalue | Infinite dimensional Hamiltonian operator k-compact operator | Eigenfunction system | Completeness | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

Russian mathematics, ISSN 1066-369X, 7/2016, Volume 60, Issue 7, pp. 37 - 46

... under
variation of the potential q(x, y).
DOI: 10.3103/S1066369X16070069
Keywords: eigenvalues, eigenfunctions, distribution and asymptotics of eigenvalues, Green
function...

eigenfunctions | completeness of a system of eigenfunctions | eigenvalues | distribution and asymptotics of eigenvalues | Mathematics, general | Mathematics | Green function

eigenfunctions | completeness of a system of eigenfunctions | eigenvalues | distribution and asymptotics of eigenvalues | Mathematics, general | Mathematics | Green function

Journal Article

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