Results 261 to 270 of about 4,257 (300)

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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Positive Powers of Positive Positive Definite Matrices

Canadian Journal of Mathematics, 1996
AbstractLet C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.
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Positive Definite Toeplitz Completions

Journal of the London Mathematical Society, 1999
Consider a partially prescribed Toeplitz matrix \(T\), that is, a Toeplitz matrix in which some diagonals are specified, while other are unspecified and may thus be treated as free variables. A completion of \(T\) is an assignment of values to the unspecified diagonals. The pattern \(P(T)\) of a partially defined Hermitian Toeplitz matrix is the set of
Johnson, Charles R., Lundquist, Michael, Nævdal, Geir   +2 more
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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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Sibling Position and Definition of Self

The Journal of Social Psychology, 1971
(1971). Sibling Position and Definition of Self. The Journal of Social Psychology: Vol. 84, No. 2, pp. 307-308.
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Positive Definite Rational Kernels

2003
Kernel methods are widely used in statistical learning techniques. We recently introduced a general kernel framework based on weighted transducers or rational relations, rational kernels, to extend kernel methods to the analysis of variable-length sequences or more generally weighted automata.
Corinna Cortes, Patrick Haffner, Mehryar Mohri   +2 more
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Inequalities for Positive Definite Functions

Mathematical Notes, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
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STRICT POSITIVE DEFINITENESS ON SPHERES

Analysis, 1999
Strictly positive definite functions on the unit sphere \(S^m\) in \(\mathbb{R}^{m+1}\) provide a tool for interpolating scattered data on \(S^m\). If there are \(n\) distinct points then strictly positive definite functions of order \(n\) are of main interest. Positive definite functions \(f\) on \(S^m\) are characterized by Schoenberg as those having
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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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