scholarly journals Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Massoud Amini ◽  
Alireza Medghalchi
Keyword(s):  
Inverse Semigroup ◽  
Harmonic Analysis ◽  
Positive Definite ◽  
Inverse Semigroups ◽  
Positive Definite Functions ◽  
Topological Groups ◽  
Topological Groupoids

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.

Bochner's Theorem and the Hausdorff Moment Theorem on foundation Topological Semigroups

1985 ◽  
Vol 37 (5) ◽  
pp. 785-809 ◽  
Author(s):  
M. Lashkarizadeh Bami
Keyword(s):  
Harmonic Analysis ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Locally Compact ◽  
Commutative Semigroups ◽  
Bochner’S Theorem ◽  
Topological Semigroups ◽  
Bochner's Theorem ◽  
Extensive Class

One of the most basic theorems in harmonic analysis on locally compact commutative groups is Bochner's theorem (see [16, p. 19]). This theorem characterizes the positive definite functions. In 1971, R. Lindhal and P. H. Maserick proved a version of Bochner's theorem for discrete commutative semigroups with identity and with an involution * (see [13]). Later, in 1980, C. Berg and P. H. Maserick in [6] generalized this theorem for exponentially bounded positive definite functions on discrete commutative semigroups with identity and with an involution *. In this work we develop these results, and also the Hausdorff moment theorem, for an extensive class of topological semigroups, the so-called “foundation topological semigroups”. We shall give examples to show that these theorems do not extend in the obvious way to general locally compact topological semigroups.

On rubin's harmonic analysis and its related positive definite functions

2012 ◽  
Vol 32 (5) ◽  
pp. 1851-1874
Author(s):  
Néji Bettaibi ◽  
Kamel Mezlini ◽  
Moufida El Guénichi
Keyword(s):  
Harmonic Analysis ◽  
Positive Definite ◽  
Positive Definite Functions

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].

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

scholarly journals A NOTE ON THE HOWSON PROPERTY IN INVERSE SEMIGROUPS

2016 ◽  
Vol 94 (3) ◽  
pp. 457-463 ◽  
Author(s):  
PETER R. JONES
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Finitely Generated ◽  
Necessary And Sufficient

An algebra has the Howson property if the intersection of any two finitely generated subalgebras is again finitely generated. A simple necessary and sufficient condition is given for the Howson property to hold on an inverse semigroup with finitely many idempotents. In addition, it is shown that any monogenic inverse semigroup has the Howson property.

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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