Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102736
Title: ON INTEGRAL ESTIMATES of NONNEGATIVE POSITIVE DEFINITE FUNCTIONS
Authors: Efimov, A.
Gaál, M.
Révész, S. G.
Issue Date: 2017
Publisher: Cambridge University Press
Citation: Efimov A. ON INTEGRAL ESTIMATES of NONNEGATIVE POSITIVE DEFINITE FUNCTIONS / A. Efimov, M. Gaál, S. G. Révész. — DOI 10.1017/S0004972717000119 // Bulletin of the Australian Mathematical Society. — 2017. — Vol. 96. — Iss. 1. — P. 117-125.
Abstract: Let l > 0 be arbitrary. We introduce the extremal quantities [equation presented] where the supremum is taken over all not identically zero nonnegative positive definite functions. We investigate how large these extremal quantities can be. This problem was originally posed by Yu. Shteinikov and S. Konyagin (for the case l = 2) and is an extension of the classical problem of Wiener. In this note we obtain exact values for the right limits limϵ0+G(k + ϵ) and limϵ0+C(k + ϵ) (k ϵ N) taken over doubly positive functions, and sufficiently close bounds for other values of l. © 2017 Australian Mathematical Publishing Association Inc.
Keywords: CONVOLUTION SQUARE
FOURIER TRANSFORM
NONNEGATIVE POSITIVE DEFINITE FUNCTION
SCHUR'S THEOREM
WIENER'S PROBLEM
URI: http://hdl.handle.net/10995/102736
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85015095246
PURE ID: 1972033
892f4831-c5dc-41b6-bde6-a32bcc0b3ec9
ISSN: 49727
DOI: 10.1017/S0004972717000119
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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