| Title:
|
Discrete spectrum and principal functions of non-selfadjoint differential operator (English) |
| Author:
|
Tunca, Gülen Başcanbaz |
| Author:
|
Bairamov, Elgiz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
689-700 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we consider the operator $L$ defined by the differential expression \[ \ell (y)=-y^{\prime \prime }+q(x) y ,\quad - \infty < x < \infty \] in $L_2(-\infty ,\infty )$, where $q$ is a complex valued function. Discussing the spectrum, we prove that $L$ has a finite number of eigenvalues and spectral singularities, if the condition \[ \sup _{-\infty < x < \infty } \Big \lbrace \exp \bigl (\epsilon \sqrt{|x|}\bigr ) |q(x)|\Big \rbrace < \infty , \quad \epsilon > 0 \] holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities. (English) |
| MSC:
|
34B24 |
| MSC:
|
34L05 |
| MSC:
|
34L15 |
| MSC:
|
34L40 |
| MSC:
|
47E05 |
| idZBL:
|
Zbl 1015.34073 |
| idMR:
|
MR1746697 |
| . |
| Date available:
|
2009-09-24T10:26:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127521 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
