Taiwanese Journal of Mathematics

ON A CONJECTURE ON THE UNIFORM CONVERGENCE OF A SEQUENCE OF WEIGHTED BOUNDED POSITIVE DEFINITE FUNCTIONS ON FOUNDATION SEMIGROUPS

M. Lashkarizadeh Bami

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Abstract

In the present paper, we shall establish one of our earlier conjectures by proving that on compact subsets of a $*$-foundation semigroup $S$ with identity and with a locally bounded Borel measurable weight function $w$, the pointwise convergence and the uniform convergence of a sequence of $w$-bounded positive definite functions on $S$ which are also continuous at the identity are equivalent..

Article information

Source
Taiwanese J. Math., Volume 2, Number 1 (1998), 87-95.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406896

Digital Object Identifier
doi:10.11650/twjm/1500406896

Mathematical Reviews number (MathSciNet)
MR1609480

Zentralblatt MATH identifier
0907.43006

Subjects
Primary: 43A35: Positive definite functions on groups, semigroups, etc. 43A10: Measure algebras on groups, semigroups, etc.

Keywords
locally compact semigroups measure algebras positive definite functions

Citation

Bami, M. Lashkarizadeh. ON A CONJECTURE ON THE UNIFORM CONVERGENCE OF A SEQUENCE OF WEIGHTED BOUNDED POSITIVE DEFINITE FUNCTIONS ON FOUNDATION SEMIGROUPS. Taiwanese J. Math. 2 (1998), no. 1, 87--95. doi:10.11650/twjm/1500406896. https://projecteuclid.org/euclid.twjm/1500406896


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