scholarly journals Strict positive definiteness on spheres via disk polynomials

2002 ◽  
Vol 31 (12) ◽  
pp. 715-724 ◽  
Author(s):  
V. A. Menegatto ◽  
A. P. Peron
Keyword(s):  
Unit Sphere ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Positive Definite Functions

We characterize complex strictly positive definite functions on spheres in two cases, the unit sphere ofℂq,q≥3, and the unit sphere of the complexℓ2. The results depend upon the Fourier-like expansion of the functions in terms of disk polynomials and, among other things, they enlarge the classes of strictly positive definite functions on real spheres studied in many recent papers.

scholarly journals On Positive Definiteness Over Locally Compact Quantum Groups

2016 ◽  
Vol 68 (5) ◽  
pp. 1067-1095 ◽  
Author(s):  
Volker Runde ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Separation Property ◽  
Locally Compact ◽  
Square Roots ◽  
Locally Compact Quantum Groups ◽  
Compact Quantum Groups ◽  
Quantum Framework

AbstractThe notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on “square roots” of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

scholarly journals Positive Definite Functions for the Class Lp(G)

1975 ◽  
Vol 27 (5) ◽  
pp. 1149-1156
Author(s):  
T. Husain ◽  
S. A. Warsi
Keyword(s):  
Compact Group ◽  
Relevant Information ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Locally Compact Group ◽  
Positive Definite Functions ◽  
Topological Groups ◽  
Locally Compact

There are several notions of positive definiteness for functions on topological groups, the two of which are: Bochner type positive definite functions and integrally positive definite functions. The class P(F) of positive definite functions for the class F can be defined more generally and it is interesting to observe that a change in F produces a different class P(F) of positive definite functions. The purpose of this paper is to study the functions in P(LP(G)) which are positive definite for the class LP(G) (1 ≦ p < ∞), where G is a compact or locally compact group. The relevant information about the class P(F) can be found in [1; 2; 3 and 8].

scholarly journals A Gneiting-Like Method for Constructing Positive Definite Functions on Metric Spaces

2020 ◽  
Author(s):  
Victor S. Barbosa ◽  
◽  
Valdir A. Menegatto ◽  
◽  
◽  
...  
Keyword(s):  
Metric Spaces ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Established Method ◽  
Bernstein Functions ◽  
Necessary And Sufficient ◽  
Complete Bernstein Functions

This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a well-established method of T. Gneiting to construct space-time positive definite functions and its many extensions. Necessary and sufficient conditions for the strict positive definiteness of the models are provided when the spaces are metric.

Strictly and Strongly Positive Definite Functions on Locally Compact Hypergroups

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
László Székelyhidi ◽  
Seyyed Mohammad Tabatabaie ◽  
Kedumetse Vati
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact

scholarly journals Approximate solutions of equations defined by complex spherical multiplier operators

2005 ◽  
Vol 2005 (2) ◽  
pp. 93-115
Author(s):  
C. P. Oliveira
Keyword(s):  
Approximate Solutions ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Sobolev Type ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Solutions Of Equations ◽  
Multiplier Operators

This paper studies, in a partial but concise manner, approximate solutions of equations defined by complex spherical multiplier operators. The approximations are from native spaces embedded in Sobolev-type spaces and derived from the use of positive definite functions to perform spherical interpolation.

scholarly journals Extension of positive definite functions

2015 ◽  
Vol 422 (1) ◽  
pp. 712-740 ◽  
Author(s):  
Palle E.T. Jorgensen ◽  
Robert Niedzialomski
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions

Positive definite functions of infinitely many variables in a layer

1972 ◽  
Vol 24 (4) ◽  
pp. 351-372 ◽  
Author(s):  
Yu. M. Berezanskii ◽  
I. M. Gali
Keyword(s):  
Positive Definite ◽  
Positive Definite Functions

PROPERTIES OF HEAT FLUX FUNCTIONS AND A LINEAR THEORY OF HEAT FLUX

1995 ◽  
Vol 09 (09) ◽  
pp. 1113-1122 ◽  
Author(s):  
LIQIU WANG
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Linear Function ◽  
Linear Theory ◽  
Strain Tensor ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Flux Vector ◽  
Heat Flux Vector

The symmetry and positive definiteness of thermal conductivity tensor K are used to derive some properties of heat flux functions ɸi (i=0, 1, 2). All ɸi are shown to be real-valued. Both ɸ0 and ɸ2 are found to be positive definite, and ɸ1 is constrained between −(ɸ0 + ɸ2) and (ɸ0 + ɸ2). By assuming heat flux vector q to be a linear function of temperature gradient ∇θ and velocity strain tensor D, ɸi reduce to three coefficients which are independent of D and ∇θ.

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