Results 201 to 210 of about 7,594,968 (240)

Complex Variable Positive Definite Functions

Complex Analysis and Operator Theory, 2013
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Jorge Buescu
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Distribution Functions and Positive-Definite Functions

The Annals of Mathematics, 1934
The distribution of the values of a real almost periodic function or more generally of an almost periodic curve in several dimensions has been investigated lately by Wintner, Haviland and others.' One of the methods applied by Wintner depends on the use of Fourier transforms and is as such a standard method in the theory of probability.
Bochner, Salomon, Jessen, B.
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On the Measurability of Positive Definite and Conditionally Positive Definite Functions

Mathematische Nachrichten, 1986
Let f be a positive definite function on a locally compact abelian group G. In this paper we show that measurability of f on an open neighbourhood of the zero implies measurability of f on G. The same result holds for conditionally positive definite functions.
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Inequalities for Positive Definite Functions

Mathematical Notes, 2020
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Positive Definite Functions and States

The Annals of Mathematics, 1954
This paper is concerned with the relation between the set P of continuous, positive definite functions on a locally compact group G and the set F of continuous, positive linear functionals on the group operator algebra A of G. This concern is motivated by an attempt to establish a connection between the procedure of Gelfand and Raikov [3] with the ...
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On Quotients of Positive Definite Functions

Acta Mathematica Hungarica, 2000
Let \(E'\) be the space of distributions with compact support and \(S\) be the space of complex valued Schwartz functions. The main result is: Let \(f:\mathbb R\to \mathbb R\) be the Fourier transform of a real \(T\in E'\). Then \(f\) is the quotient of two positive definite functions from \(S\) if and only if \(f(0)\neq 0\).
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Addendum to the Paper „On the Measurability of Positive Definite and Conditionally Positive Definite Functions”︁

Mathematische Nachrichten, 1987
The aim of this note is to simplify the proof of Theorem 1 [(*)\ ibid. 125, 239-242 (1986; Zbl 0605.43004)] and to extend the results of (*) to arbitrary locally compact groups.
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Positive Definiteness of Generalized Homogeneous Functions

IFAC Proceedings Volumes, 2013
Identification of positive definiteness of functions is crucial in control theory. However for generalized homogeneous functions, there does not exist an effective method to identify the positive definiteness. In this paper, we consider Lipschitz continuous generalized homogeneous functions.
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Strictly positive definite functions on spheres

Journal of Approximation Theory
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