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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 004, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.004 (Mi sigma1440) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions

Pier Giovanni Bissiria, Valdir A. Menegattob, Emilio Porcuca

a School of Mathematics & Statistics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
b Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brazil
c Department of Mathematics, University of Atacama, Copiapó, Chile
Full-text PDF (351 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2019.004
Abstract: Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been studied by several mathematicians in the last years. This paper provides a set of relations between Schoenberg sequences defined over real as well as complex spheres of different dimensions. We illustrate our findings describing an application to strict positive definiteness.
Keywords: positive definite; Schoenberg pair; spheres; strictly positive definite.
Funding agency Grant number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2016/09906-0
Fondo Nacional de Desarrollo Científico y Tecnológico 1130647
Research of Valdir A. Menegatto was partially supported by FAPESP, grant 2016/09906-0. Emilio Porcu is partially supported by grant FONDECYT 1130647 from Chilean Ministry of Education, and by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, grant “Millenium Nucleus Center for the Discovery of Structures in Complex Data”.
Received: July 25, 2018; in final form January 18, 2019; Published online January 23, 2019
Bibliographic databases:
Document Type: Article
MSC: 33C45; 42A16; 42A82; 42C10
Language: English
Citation: Pier Giovanni Bissiri, Valdir A. Menegatto, Emilio Porcu, “Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions”, SIGMA, 15 (2019), 004, 12 pp.
Citation in format AMSBIB
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\paper Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions
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\vol 15
\papernumber 004
\totalpages 12
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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