منابع مشابه
Extending Positive Definiteness
The main result of this paper gives criteria for extendibility of mappings defined on symmetric subsets of ∗-semigroups to positive definite ones. By specifying the mappings in question we obtain new solutions of relevant issues in harmonic analysis concerning truncations of some important multivariate moment problems, like complex, two-sided complex and multidimensional trigonometric moment pr...
متن کاملDifferential Criteria for Positive Definiteness
We show how the Mellin transform can be used to derive differential criteria for integral representations of functions as scale mixtures, and apply this idea to derive differential criteria for positive definiteness of functions in a manner similar to that of Gneiting (1999,2001). We also give a simple derivation of Williamson’s result on multiply monotone functions (Williamson, 1956), with a l...
متن کاملComputational Geometry of Positive Definiteness
In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as that of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task bec...
متن کاملPositive Definiteness of Generalized Homogeneous Functions
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. For the functions, we propose a new method to identify the positive definiteness of the functions. Moreo...
متن کاملPositive-definiteness, Integral Equations and Fourier Transforms
We show that positive definite kernel functions k(x, y), if continuous and integrable along the main diagonal, coincide with kernels of positive integral operators in L2(R). Such an operator is shown to be compact; under the further assumption k(x, x) → 0 as |x| → ∞ it is also trace class and the corresponding bilinear series converges absolutely and uniformly. If k1/2(x, x) ∈ L1(R), all these ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-2010-05268-7