Characterization of Strict Positive Definiteness on products of complex spheres: Characterization of strict positive definiteness on products of complex spheres
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| Názov: | Characterization of Strict Positive Definiteness on products of complex spheres: Characterization of strict positive definiteness on products of complex spheres |
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| Autori: | Mario H. Castro, Eugenio Massa, Ana Paula Peron |
| Zdroj: | Positivity. 23:853-874 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Springer Science and Business Media LLC, 2019. |
| Rok vydania: | 2019 |
| Predmety: | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), 42A82, 42C10, Mathematics - Classical Analysis and ODEs, product of complex spheres, generalized Zernike polynomial, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Positive definite functions in one variable harmonic analysis, strictly positive definite functions, Positive definite functions on groups, semigroups, etc |
| Popis: | In this paper we consider Positive Definite functions on products $��_{2q}\times��_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and sufficient for the function to be Strictly Positive Definite. The result includes also the more delicate cases in which $p$ and/or $q$ can be $1$ or $\infty$. The condition we obtain states that a suitable set in $\mathbb{Z}^2$, containing the indexes of the strictly positive coefficients in the expansion, must intersect every product of arithmetic progressions. |
| Druh dokumentu: | Article Other literature type |
| Popis súboru: | application/xml |
| Jazyk: | English |
| ISSN: | 1572-9281 1385-1292 |
| DOI: | 10.1007/s11117-018-00641-5 |
| DOI: | 10.48550/arxiv.1803.06264 |
| Prístupová URL adresa: | http://arxiv.org/pdf/1803.06264 http://arxiv.org/abs/1803.06264 https://zbmath.org/7118383 https://doi.org/10.1007/s11117-018-00641-5 http://ui.adsabs.harvard.edu/abs/2018arXiv180306264C/abstract https://arxiv.org/abs/1803.06264 https://arxiv.org/pdf/1803.06264.pdf https://link.springer.com/article/10.1007/s11117-018-00641-5 |
| Rights: | Springer TDM arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....fba7cdf0147c69de109f49e5dd84fb9d |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | In this paper we consider Positive Definite functions on products $��_{2q}\times��_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and sufficient for the function to be Strictly Positive Definite. The result includes also the more delicate cases in which $p$ and/or $q$ can be $1$ or $\infty$. The condition we obtain states that a suitable set in $\mathbb{Z}^2$, containing the indexes of the strictly positive coefficients in the expansion, must intersect every product of arithmetic progressions. |
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| ISSN: | 15729281 13851292 |
| DOI: | 10.1007/s11117-018-00641-5 |