Hostname: page-component-cb9f654ff-hn9fh Total loading time: 0 Render date: 2025-08-23T08:02:47.795Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive Definite Functions for the Class Lp (G)

Published online by Cambridge University Press:  20 November 2018

T. Husain  and
S. A. Warsi
T. Husain
Affiliation:
McMaster University, Hamilton, Ontario
S. A. Warsi
Affiliation:
McMaster University, Hamilton, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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].

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1149 - 1156
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Cooper, J. L. B., Positive-definite functions of a real variable, Proc. London, Math. Soc. 10 (1960), 53–66.Google Scholar
2. Edwards, R. E., Unbounded integrally positive definite functions, Studia Math. 33 (1969), 185–191.Google Scholar
3. Hewitt, Edwin and Stromberg, Karl, Real and abstract analysis (Springer Verlag, New York 1965).Google Scholar
4. Hewitt, Edwin and Ross, K. A., Abstract harmonic analysis Vol. I (Heidelberg and New York, 1963).Google Scholar
5. Hewitt, Edwin and Ross, K. A., Integrally positive definite functions, Studia Mathematica 31 (1969), 145–151.Google Scholar
6. Husain, Taqdir, Introduction to topological groups (W. B. Saunders Company, Philadelphia and London 1966).Google Scholar
7. Naimark, M. A., Normed rings (Noordhoff, Groningen 1961).Google Scholar
8. Stewart, James, Unbounded positive definite functions, Can. J. Math. 21 (1969), 1309–1318.Google Scholar