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

Hayati Olğar; Oktay Mukhtarov

Makale detayları

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

Yazarlar:

Hayati Olğar | Oktay Mukhtarov

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338163

pISSN:

1304-7981

Anahtar kelimeler:

Özet:

 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.

Makale detayları

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

Yazarlar:

Hayati Olğar | Oktay Mukhtarov

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338163

pISSN:

1304-7981

Spectral problem

Boundary conditions

Jump conditions

Eigenvalues

Weak eigenfunctions

Sayı

Makale detayları

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

Yazarlar: Hayati Olğar | Oktay Mukhtarov

Yayıncı: Tokat Gaziosmanpasa University

Ana Başlıklar: Operator Algebras and Functional Analysis | Applied Mathematics (Other)

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

Belge Tipi: Makale

Yayın Tarihi: 12/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001338163

pISSN: 1304-7981

Spectral problem

Boundary conditions

Jump conditions

Eigenvalues

Weak eigenfunctions

Sayı

Yazarlar:

Hayati Olğar | Oktay Mukhtarov

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Operator Algebras and Functional Analysis | Applied Mathematics (Other)

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

12/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001338163

pISSN:

1304-7981