In a recent paper [15], Hilbert space operators T with the property that each sequence of form {‖Tnh‖2}n=0∞ is conditionally positive definite in semigroup sense were introduced. present paper, this line research continued depth case unilateral weighted shifts. The conditional definiteness shifts characterized terms formal moment sequences. description representing triplet, main object canonica...

I t i s well-known t h a t k r i g i n g and i n t e r p o l a t i o n by s p l i n e s a r e e q u i v a l e n t . Kr ig ing i s based on a s t o c h a s t i c f o r m u l a t i o n whereas s p l i n e s a r e f o r m u l a t e d I n a d e t e r m i n i s t i c way. A t h i r d p r e s e n t a t i o n i s g i v e n i n terms of Rad ia l P a s i s F u n c t i o n s . The c n n n e c t l o n s b...

We prove that every scalar valued positive definite function f , on a generalized interval of an ordered group, has a positive definite extension to the whole group. We also prove that if f is continuous (measurable), then every positive definite extension of f is continuous (measurable). Additionally we obtain a representation result for the measurable case.

Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...

In the FindCandidates function (line 4), Select finds all the single edges that can be added to the current mask graph GΩ while maintaining its chordal structure. To do that, we make use of the clique tree data structure as introduced by Ibarra [1]. Given a graph G = (V,E), the clique tree is a tree C = (VC , EC), in which each node is a maximal clique of G, i.e., VC ⊂ 2 . In our case the numbe...

we study harmonic analysis on cocommutative kpc-hyper-groups‎, which is a generalization of djs-hypergroups‎, ‎introduced by kalyuzhnyi‎, ‎podkolzin and chapovsky‎. ‎we prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a radon measure on kpc-hypergroup $q$ and $gamma$ is a character on $q$.