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Complex analysis and operator theory, ISSN 1661-8262, 08/2018, Volume 13, Issue 3, pp. 1111 - 1131
Journal Article
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
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
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2009, Volume 70, Issue 12, pp. 4123 - 4139
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
Journal Article
Iranian journal of science and technology. Transaction A, Science, ISSN 1028-6276, 3/2016, Volume 40, Issue 1, pp. 1 - 8
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 12/2006, Volume 134, Issue 12, pp. 3487 - 3494
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
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
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
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
Journal Article
Chinese physics B, ISSN 1674-1056, 2011, Volume 20, Issue 12, pp. 264 - 272
Journal Article
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
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
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
Journal Article
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