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On Certain Functions With Positive Definite Hessian

The Annals of Mathematics, 1960
If 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, 1956
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Positive Definite Functions on Separable Function Spaces

1996
A notion of a separable function space is defined. It is proved that a positive definite function on the semigroup of the positive elements of a separable function space is the Laplace transform of a measure concentrated on the set of positive functionals.
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On Generalized Positive-Definite Functions

Proceedings of the London Mathematical Society, 1965
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Weinstein positive definite functions

Positivity, 2017
Khaled Mehrez
exaly  

On differentiability and analyticity of positive definite functions

Journal of Mathematical Analysis and Applications, 2011
Jorge Buescu
exaly  

Positive and Positive-Definite Generalized Functions

1964
I.M. GEL'FAND, N.Ya. VILENKIN
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