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On the Measurability of Positive Definite and Conditionally Positive Definite Functions
Mathematische Nachrichten, 1986Let 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, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Positive Definite Functions and States
The Annals of Mathematics, 1954This 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, 2000Let \(E'\) 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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Positive Definite Functions and Operator Inequalities
Bulletin of the London Mathematical Society, 2000Positive 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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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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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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Complex Variable Positive Definite Functions
Complex Analysis and Operator Theory, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Buescu, Jorge, Paixão, António
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Positive Definiteness of Generalized Homogeneous Functions
IFAC Proceedings Volumes, 2013Identification 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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On Certain Functions With Positive Definite Hessian
The Annals of Mathematics, 1960If u = u(x, y) is a C" solution of rt - 82 = 1 in the whole E2, then u is a quadratic polynomial. It turns out that the neat proof of Nitsche can be extended to prove a generalization of this result to several variables. THEOREM. Let u = u(x1, - * *, xn) be a C" function on El.
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On Positive-Definite Functions
Proceedings of the London Mathematical Society, 1956openaire +1 more source