A Polya criterion for (strict) positive-definiteness on the sphere

Strict Positive Definiteness on Spheres via Disk Polynomials

Differential 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...

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...

Strict key avalanche criterion

A block cipher, such as the DES cipher, is used to encrypt binary plaintext in discrete blocks of length n using a key of length m, to form ciphertext blocks of length n. A block cipher is said to satisfy the strict key avalanche criterion if a one bit change in the key causes on the average one half of the ciphertext bit positions to change. In this paper the importance of the strict key avala...

Computational 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...