A Classical Theorem on the Singularities of Legendre Series in C3 and Associated System of Hyperbolic Partial Differential Equations
A classical theorem of Nehari relates the singularities of Legendre series expansions in $C_z$ with those of associated Taylor's series in $C_t$. The generalization of Nehari's theorem is known for Legendre series in $C_{z_1 \times z_2}$. In this paper, function theoretic methods develop t...
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| Veröffentlicht in: | SIAM journal on mathematical analysis Jg. 28; H. 3; S. 704 - 714 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
01.05.1997
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| Schlagworte: | |
| ISSN: | 0036-1410, 1095-7154 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A classical theorem of Nehari relates the singularities of Legendre series expansions in $C_z$ with those of associated Taylor's series in $C_t$. The generalization of Nehari's theorem is known for Legendre series in $C_{z_1 \times z_2}$. In this paper, function theoretic methods develop the analogous relationships between the singularities of series expanded as triple products of Legendre polynomials in $C_{z_1 \times z_2 \times z_3}$ and those of associated analytic functions in $C_t$. The singularities of these generalized Legendre series are determined by certain elliptic curves. Moreover, these series satisfy a system of hyperbolic partial differential equations (PDEs) in $C^3$ that are connected to Bochner's study of Poisson processes in $R^2$. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0036-1410 1095-7154 |
| DOI: | 10.1137/S0036141094273490 |