The basis property of generalized eigenfunctions for one boundary value problem with discontinuities at two interior points

Hayati Olğar; Oktay Mukhtarov

Article Details

The basis property of generalized eigenfunctions for one boundary value problem with discontinuities at two interior points

Authors:

Hayati Olğar | Oktay Mukhtarov

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Journal:

Journal of New Results in Science Vol.13 Issue 3, pp.221-231

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001338163

pISSN:

1304-7981

Keywords:

Abstract:

 In this study, we consider a spectral problem for one boundary value problem with discontinuities at two interior points. The boundary conditions involve a spectral parameter. We consider some compact, positive, self-adjoint operators to reduce the spectral problem to an operator-pencil equation. Then, it was proven that this operator-pencil is positive definite, the spectrum is discrete, and the system of weak eigenfunctions forms a Riesz basis of the appropriate Sobolev space.

 In this study, we consider a spectral problem for one boundary value problem with discontinuities at two interior points. The boundary conditions involve a spectral parameter. We consider some compact, positive, self-adjoint operators to reduce the spectral problem to an operator-pencil equation. Then, it was proven that this operator-pencil is positive definite, the spectrum is discrete, and the system of weak eigenfunctions forms a Riesz basis of the appropriate Sobolev space.

 In this study, we consider a spectral problem for one boundary value problem with discontinuities at two interior points. The boundary conditions involve a spectral parameter. We consider some compact, positive, self-adjoint operators to reduce the spectral problem to an operator-pencil equation. Then, it was proven that this operator-pencil is positive definite, the spectrum is discrete, and the system of weak eigenfunctions forms a Riesz basis of the appropriate Sobolev space.

 In this study, we consider a spectral problem for one boundary value problem with discontinuities at two interior points. The boundary conditions involve a spectral parameter. We consider some compact, positive, self-adjoint operators to reduce the spectral problem to an operator-pencil equation. Then, it was proven that this operator-pencil is positive definite, the spectrum is discrete, and the system of weak eigenfunctions forms a Riesz basis of the appropriate Sobolev space.

Article Details

The basis property of generalized eigenfunctions for one boundary value problem with discontinuities at two interior points

Authors:

Hayati Olğar | Oktay Mukhtarov

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Journal:

Journal of New Results in Science Vol.13 Issue 3, pp.221-231

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001338163

pISSN:

1304-7981

Spectral problem

Boundary conditions

Jump conditions

Eigenvalues

Weak eigenfunctions

Issues

Article Details

The basis property of generalized eigenfunctions for one boundary value problem with discontinuities at two interior points

Authors: Hayati Olğar | Oktay Mukhtarov

Publisher: Tokat Gaziosmanpasa University

Main Topics: Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Journal: Journal of New Results in Science Vol.13 Issue 3, pp.221-231

Document Type: Article

Publication Date: 12/2024

Document Language: English

Document ID (Org No.): 2001338163

pISSN: 1304-7981

Spectral problem

Boundary conditions

Jump conditions

Eigenvalues

Weak eigenfunctions

Issues

Authors:

Hayati Olğar | Oktay Mukhtarov

Publisher:

Tokat Gaziosmanpasa University

Main Topics:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Journal:

Journal of New Results in Science Vol.13 Issue 3, pp.221-231

Document Type:

Article

Publication Date:

12/2024

Document Language:

English

Document ID (Org No.):

2001338163

pISSN:

1304-7981