Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces
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Títol
Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spacesData de publicació
2022-07-11Editor
Elsevier Inc.ISSN
0022-247XCita bibliogràfica
Barbosa, V. S., Gregori, P., Peron, A. P., & Porcu, E. (2022). Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces. Journal of Mathematical Analysis and Applications, 516(1), 126487.Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
Geodesically isotropic positive definite functions on compact two-point homogeneous
spaces of dimension d have series representation as members of weighted Lebesgue
spaces Lw
1 ([−1, 1]), where the weight w(x) = ... [+]
Geodesically isotropic positive definite functions on compact two-point homogeneous
spaces of dimension d have series representation as members of weighted Lebesgue
spaces Lw
1 ([−1, 1]), where the weight w(x) = wα,β(x) = (1 − x)α(1 + x)β is the one
related to the Jacobi orthogonal polynomials P(α,β)(x) in [−1, 1], and the exponents
α and β are related to the dimension d. We derive some recurrence relations among
the coefficients of the series representations under different exponents, and we apply
them to prove inheritance of positive definiteness between dimensions. Additionally,
we give bounds on the curvature at the origin of such positive definite functions
with compact support, extending the existing solutions from d-dimensional spheres
to compact two-point homogeneous spaces. [-]
Publicat a
Journal of Mathematical Analysis and Applications, Vol. 516, Issue 1 (December 2022)Entitat finançadora
Agencia Estatal de Investigación (España) | Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq (Brazil) | FAPESP, Brazil | Khalifa University of Science and Technology (Abu Dhabi, UAE)
Codi del projecte o subvenció
PID2019-107392RB-I00 | 203033/2019-1 | 2021/04269-0 | FSU-2021-016
Drets d'accés
© 2022 The Author(s).
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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