Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization
We describe the relationship between the expansion of a self-adjoint operator in generalized eigenvectors and the direct integral of Hilbert spaces. We perform the explicit diagonalization of a self-adjoint absolutely continuous singular integral operator Y using an Hermitian nonnegative kernel cons...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3896 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510027443339264 |
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| author | Vorob'ev, I. V. Воробйов, І. В. |
| author_facet | Vorob'ev, I. V. Воробйов, І. В. |
| author_sort | Vorob'ev, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:14:44Z |
| description | We describe the relationship between the expansion of a self-adjoint operator in generalized eigenvectors and the direct integral of Hilbert spaces. We perform the explicit diagonalization of a self-adjoint absolutely continuous singular integral operator Y using an Hermitian nonnegative kernel consisting of boundary values of the determining function of the operator T = X + iY with respect to the resolvent of the imaginary part of Y. |
| first_indexed | 2026-03-24T02:50:28Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3896 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:50:28Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/de/281025b0495bc5e6c2f97847857678de.pdf |
| spelling | umjimathkievua-article-38962020-03-18T20:14:44Z Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization Разложение по обобщенным собственным векторам и диагонализация самосопряженного абсолютно непрерывного сингулярного интегрального оператора Vorob'ev, I. V. Воробйов, І. В. We describe the relationship between the expansion of a self-adjoint operator in generalized eigenvectors and the direct integral of Hilbert spaces. We perform the explicit diagonalization of a self-adjoint absolutely continuous singular integral operator Y using an Hermitian nonnegative kernel consisting of boundary values of the determining function of the operator T = X + iY with respect to the resolvent of the imaginary part of Y. Описано зв'язок між розкладанням самоспряженого оператора за узагальненими власними векторами та прямим інтегралом гільбертових просторів. Проведено явну діагопалізацію самоспряженого абсолютно неперервного сингулярного інтегрального оператора $Y$ за допомогою ермітово-невід'ємного ядра, складеного із межових значень визначальної функції оператора $Т = X + iY$ відносно резольвенти уявної частини $Y$. Institute of Mathematics, NAS of Ukraine 2003-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3896 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 1 (2003); 138-145 Український математичний журнал; Том 55 № 1 (2003); 138-145 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3896/4507 https://umj.imath.kiev.ua/index.php/umj/article/view/3896/4508 Copyright (c) 2003 Vorob'ev I. V. |
| spellingShingle | Vorob'ev, I. V. Воробйов, І. В. Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title | Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title_alt | Разложение по обобщенным собственным векторам и диагонализация самосопряженного абсолютно непрерывного сингулярного интегрального оператора |
| title_full | Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title_fullStr | Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title_full_unstemmed | Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title_short | Expansion of a Self-Adjoint Absolutely Continuous Singular Integral Operator in Generalized Eigenvectors and Its Diagonalization |
| title_sort | expansion of a self-adjoint absolutely continuous singular integral operator in generalized eigenvectors and its diagonalization |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3896 |
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