Extension of positive definite functions and representation of functions in terms of spherical functions in symmetric spaces of noncompact type of rank 1

1975 ◽  
Vol 215 (2) ◽  
pp. 97-116 ◽  
Author(s):  
A. Edward Nussbaum
Keyword(s):  
Symmetric Spaces ◽  
Positive Definite ◽  
Spherical Functions ◽  
Positive Definite Functions ◽  
Noncompact Type

Some Convexity Results for the Cartan Decomposition

2003 ◽  
Vol 55 (5) ◽  
pp. 1000-1018 ◽  
Author(s):  
P. Graczyk ◽  
P. Sawyer
Keyword(s):  
Symmetric Spaces ◽  
Singular Values ◽  
Product Formula ◽  
Spherical Functions ◽  
Cartan Decomposition ◽  
Simple Description ◽  
Noncompact Type

AbstractIn this paper, we consider the set = a(eXKeY) where a(g) is the abelian part in the Cartan decomposition of g. This is exactly the support of the measure intervening in the product formula for the spherical functions on symmetric spaces of noncompact type. We give a simple description of that support in the case of SL(3; F) where F= R, Cor H. In particular, we show that is convex.We also give an application of our result to the description of singular values of a product of two arbitrary matrices with prescribed singular values.

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

Scattering theory for symmetric spaces of noncompact type

1993 ◽  
Vol 72 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Ralph S. Phillips ◽  
Mehrdad M. Shahshahani
Keyword(s):  
Scattering Theory ◽  
Symmetric Spaces ◽  
Noncompact Type

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
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