On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis
We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3...
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| Datum: | 2001 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4311 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510441875177472 |
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| author | Kalyuzhnyi, A. A. Kachanovskii, N. A. Калюжный, А. А. Качановский, Н. А. Калюжный, А. А. Качановский, Н. А. |
| author_facet | Kalyuzhnyi, A. A. Kachanovskii, N. A. Калюжный, А. А. Качановский, Н. А. Калюжный, А. А. Качановский, Н. А. |
| author_sort | Kalyuzhnyi, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:26:34Z |
| description | We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ in the model one-dimensional case. The main results are a detailed intrinsic description of spaces of test functions, a description of generalized translation operators, and the investigation of integral C- and S-transformations. |
| first_indexed | 2026-03-24T02:57:03Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4311 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:57:03Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/66/29b95963dd3336ed4ed8be5d96e0cb66.pdf |
| spelling | umjimathkievua-article-43112020-03-18T20:26:34Z On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis Об ортогональных квазиаппелевых полиномах в негауссовом анализе Kalyuzhnyi, A. A. Kachanovskii, N. A. Калюжный, А. А. Качановский, Н. А. Калюжный, А. А. Качановский, Н. А. We study an example of the construction of a non-Gaussian analysis using orthogonal generalized Appell-like polynomials with the generating function $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ in the model one-dimensional case. The main results are a detailed intrinsic description of spaces of test functions, a description of generalized translation operators, and the investigation of integral C- and S-transformations. Вивчається приклад побудови негауссівського аналізу за допомогою ортогональних узагальнених квазіаппелевих поліномів з твірною функцією $$\frac{1}{{\sqrt {1 - 2a{\lambda + \lambda }^{2}} } }\cos \left( {\sqrt x \frac{1}{2}\int\limits_{0}^{\lambda } {\frac{{du}}{{\sqrt {u - 2au^2 + u^3 } }}} } \right),\quad a >1,$$ у модельному одновимірному випадку. Основними результатами є докладний внутрішній опис просторів основних функцій, опис операторів узагальненого зсуву та вивчення інтегральних $C$-та $S$-перетворень. Institute of Mathematics, NAS of Ukraine 2001-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4311 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 7 (2001); 892-907 Український математичний журнал; Том 53 № 7 (2001); 892-907 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4311/5326 https://umj.imath.kiev.ua/index.php/umj/article/view/4311/5327 Copyright (c) 2001 Kalyuzhnyi A. A.; Kachanovskii N. A. |
| spellingShingle | Kalyuzhnyi, A. A. Kachanovskii, N. A. Калюжный, А. А. Качановский, Н. А. Калюжный, А. А. Качановский, Н. А. On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title | On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title_alt | Об ортогональных квазиаппелевых полиномах
в негауссовом анализе |
| title_full | On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title_fullStr | On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title_full_unstemmed | On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title_short | On Orthogonal Appell-Like Polynomials in Non-Gaussian Analysis |
| title_sort | on orthogonal appell-like polynomials in non-gaussian analysis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4311 |
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