An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution
We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of the -hypergeometric function of type ₂₁. The orthogonality measure is the wrapped geometric distribution. Some ''classical'' properties...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211079 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution. Alexei Zhedanov. SIGMA 16 (2020), 140, 9 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705953893253120 |
|---|---|
| author | Zhedanov, Alexei |
| author_facet | Zhedanov, Alexei |
| citation_txt | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution. Alexei Zhedanov. SIGMA 16 (2020), 140, 9 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of the -hypergeometric function of type ₂₁. The orthogonality measure is the wrapped geometric distribution. Some ''classical'' properties of the above polynomials are presented.
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| first_indexed | 2026-03-18T23:20:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211079 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T23:20:15Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhedanov, Alexei 2025-12-23T13:11:20Z 2020 An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution. Alexei Zhedanov. SIGMA 16 (2020), 140, 9 pages 1815-0659 2020 Mathematics Subject Classification: 33D45; 42C05 arXiv:2010.10321 https://nasplib.isofts.kiev.ua/handle/123456789/211079 https://doi.org/10.3842/SIGMA.2020.140 We present a new explicit family of polynomials orthogonal on the unit circle with a dense point spectrum. This family is expressed in terms of the -hypergeometric function of type ₂₁. The orthogonality measure is the wrapped geometric distribution. Some ''classical'' properties of the above polynomials are presented. The author is indebted to F.A. Grunbaum, A. Magnus, V. Spiridonov, S. Tsujimoto, and L. Vinet for discussions and to anonymous referees for valuable remarks. The author is gratefully holding Simons CRM Professorship and is funded by the National Foundation of China (Grant No. 11771015). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution Article published earlier |
| spellingShingle | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution Zhedanov, Alexei |
| title | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution |
| title_full | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution |
| title_fullStr | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution |
| title_full_unstemmed | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution |
| title_short | An Explicit Example of Polynomials Orthogonal on the Unit Circle with a Dense Point Spectrum Generated by a Geometric Distribution |
| title_sort | explicit example of polynomials orthogonal on the unit circle with a dense point spectrum generated by a geometric distribution |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211079 |
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