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Harmonic Analysis on Semigroups
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On sets of Haar measure zero in abelian polish groups
It is shown that the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact. It turns out that these groups, in many respects,…
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Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- 1. Locally Convex Vector Spaces.- 2. Hahn-Banach Theorems.- 3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and…
On the existence of pathological submeasures and the construction of exotic topological groups
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Functions operating on positive definite matrices and a theorem of Schoenberg
We prove that the set of all functions/: [-1, l]-»[-l, 1] operating on real positive definite matrices and normalized such that/(l) = 1, is a Bauer simplex, and we identify its extreme points. As an…
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A remark on the multidimensional moment problem
To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued…
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Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings
Some recent results of Namioka on strong continuity of weakly continuous mappings (in a dense G3 set) and results of R. E. Johnson on norm separability of the range of such mappings (under conditions…
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On Some Measures Analogous to Haar Measure.
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Joint continuity of separately continuous functions
ABsmRAcr. It is shown that a separately continuous function f: X x Y -+ Z from the product of a certain type of Hausdorff space X and a compact Hausdorff space Y into a metrizable space Z is jointly…
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Positive definite functions on Abelian semigroups
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