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Strictly Positive Definite Functions [PDF]
Journal of Approximation Theory, 1996 A complex-valued continuous function defined on \(\mathbb{R}\) is said to be strictly positive definite on \(\mathbb{R}\) if the \(n\) by \(n\) matrix \((f(x_i- x_j))\) is positive definite for all choices of pairwise distinct points \(x_1,x_2,\dots,x_n\in\mathbb{R}\), and all \(n\geq 1\).
Chang, Kuei-Fang
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Zastavnyi operators and positive definite radial functions [PDF]
Statistics and Probability Letters, 2020 \ua9 2019 Elsevier B.V. We consider a new operator acting on rescaled weighted differences between two members of the class Φd of positive definite radial functions.
Moreno Bevilacqua +2 more
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Stable positive definite functions [PDF]
Transactions of the American Mathematical Society, 1975 This paper investigates the stability of positive definite functions on locally compact groups under one parameter groups of automorphisms. As an application of this it is shown that the only probability distributions on
Parthasarathy, K. R., Schmidt, K.
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On positive positive-definite functions and Bochner’s Theorem
Journal of Complexity, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan Vybíral
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On matrix valued square integrable positive definite functions [PDF]
Monatshefte Fur Mathematik, 2015 . In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on L2 positive definite functions. We show that a matrix-valued continuous L2 positive definite function can always
Hongyu He
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Unbounded Positive Definite Functions
Canadian Journal of Mathematics, 1969 Let G be an abelian group, written additively. A complexvalued function ƒ, defined on G, is said to be positive definite if the inequality1holds for every choice of complex numbers C1, …, cn and S1, …, sn in G. It follows directly from (1) that every positive definite function is bounded. Weil (9, p.
James Stewart
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Positive Definite Functions and Operator Inequalities [PDF]
Bulletin of the London Mathematical Society, 2000 Positive definite functions arise in various areas of mathematical analysis such as classical interpolation problems, the Loewner theory of monotone operator functions, operator inequalities and others. The present paper has two objectives. The first is to present and to advance a technique for proving the positive definiteness of some classes of ...
Bhatia, Rajendra, Parthasarathy, K. R.
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Strictly Hermitian positive definite functions [PDF]
Journal d'Analyse Mathématique, 2004 Let H be any complex inner product space with inner product . We say that f : C -->C is Hermitian positive definite on H if the matrix $$(f())_{r,s=1}^n \eqno(*)$$ is Hermitian positive definite for all choice of z^1,...,z^n in H, all n. It is strictly Hermitian positive definite if the matrix (*) is also non-singular for any choice of distinct z^1,.
Allan Pinkus
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Extensions of positive definite functions on free groups [PDF]
Journal of Functional Analysis, 2007 An analogue of Krein's extension theorem is proved for operator-valued positive definite functions on free groups. The proof gives also the parametrization of all extensions by means of a generalized type of Szegö parameters.
Timotin, D. +3 more
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On unbounded positive definite functions [PDF]
, 2018 It is well known that positive definite functions are bounded, taking their maximum absolute value at 0. Nevertheless, there are unbounded functions, arising e.g. in potential theory or the study of (continuous) extremal measures, which still exhibit the
Phillips, Tomos, Schmidt, Karl Michael
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