Generalized Fourier Series as Green’s Function Expansion for Multi-interval Sturm–Liouville Systems

被引：0

作者：

K. Aydemir

O. Sh. Mukhtarov

机构：

[1] Amasya University,Department of Mechanical Engineering, Technology Faculty

[2] Gaziosmanpaşa University,Department of Mathematics, Faculty of Arts and Science

[3] Azerbaijan National Academy of Sciences,Institute of Mathematics and Mechanics

来源：

Mediterranean Journal of Mathematics | 2017年 / 14卷

关键词：

Sturm–Liouville problems; Green’s function; transmission conditions; resolvent operator; Fourier series; 34B24; 34B27;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This study aims to investigate a class of boundary-value transmission problems consisting of Sturm–Liouville equation on finite number disjoint intervals together with eigenparameter-dependent boundary conditions and supplementary transmission conditions at the interior transmittal points. We introduce new Hilbert spaces for self-adjoint realization of the problem, and state the main spectral properties of eigenvalues and eigenfunctions of the considered problem. Then by suggesting own approaches, we have presented a formula for Green’s function and resolvent operator. Finally, we find the resolvent function for corresponding inhomogeneous problem and establish completeness relation of eigenfunctions as generalized Fourier series.

引用

共 50 条

[21] Divergence of the Fourier series by generalized Haar systems at points of continuity of a function
Shcherbakov V.I.
Russian Mathematics, 2016, 60 (1) : 42 - 59
[22] General form of the Green's function regular at infinity for the homogeneous Sturm-Liouville matrix operator
Pernas-Salomon, Rene
Perez-Alvarez, R.
Velasco, V. R.
APPLIED MATHEMATICS AND COMPUTATION, 2015, 269 : 824 - 833
[23] The Spectral Expansion on the Entire Real Line of Green's Function for a Two-Layer Medium in the Eigenfunctions of a Nonself-Adjoint Sturm–Liouville Operator
E. G. Saltykov
Differential Equations, 2002, 38 : 726 - 730
[24] A Perturbation Analysis for General Nonlinear Continuous Systems Using Fourier Series and Green’s Function Method
S. A. A. Hosseini
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2021, 45 : 1103 - 1114
[25] A Perturbation Analysis for General Nonlinear Continuous Systems Using Fourier Series and Green's Function Method
Hosseini, S. A. A.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF MECHANICAL ENGINEERING, 2021, 45 (04) : 1103 - 1114
[26] The spectral expansion on the entire real line of Green's function for a two-layer medium in the eigenfunctions of a nonself-adjoint Sturm-Liouville operator
Saltykov, EG
DIFFERENTIAL EQUATIONS, 2002, 38 (05) : 726 - 730
[27] Generalized Sturm expansions of the Coulomb Green’s function and two-photon Gordon formulas
A. A. Krylovetsky
N. L. Manakov
S. I. Marmo
Journal of Experimental and Theoretical Physics, 2001, 92 : 37 - 60
[28] Generalized Sturm expansions of the Coulomb Green's function and two-photon Gordon formulas
Krylovetsky, AA
Manakov, NL
Marmo, SI
JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS, 2001, 92 (01) : 37 - 60
[29] Series expansion of a function's expectation matrix at the zero interval length limit
Demiralp, Metin
Numerical Analysis and Applied Mathematics, 2007, 936 : 155 - 158
[30] The spectral expansion on the entire real line of Green's function for a three-layer medium in the fundamental functions of a nonself-adjoint Sturm-Liouville operator
Saltykov, E. G.
PIERS 2006 Cambridge: Progress in Electromagnetics Research Symposium, Proceedings, 2006, : 344 - 346

← 1 2 3 4 5 →