Academic Journal
Characterization of Strict Positive Definiteness on products of complex spheres: Characterization of strict positive definiteness on products of complex spheres
| Τίτλος: | Characterization of Strict Positive Definiteness on products of complex spheres: Characterization of strict positive definiteness on products of complex spheres |
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| Συγγραφείς: | Mario H. Castro, Eugenio Massa, Ana Paula Peron |
| Πηγή: | Positivity. 23:853-874 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Springer Science and Business Media LLC, 2019. |
| Έτος έκδοσης: | 2019 |
| Θεματικοί όροι: | 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 |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | Article Other literature type |
| Περιγραφή αρχείου: | application/xml |
| Γλώσσα: | English |
| ISSN: | 1572-9281 1385-1292 |
| DOI: | 10.1007/s11117-018-00641-5 |
| DOI: | 10.48550/arxiv.1803.06264 |
| Σύνδεσμος πρόσβασης: | 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 |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....fba7cdf0147c69de109f49e5dd84fb9d |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 15729281 13851292 |
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| DOI: | 10.1007/s11117-018-00641-5 |