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Pseudo-Measure Energy and Spectral Synthesis

Published online by Cambridge University Press:  20 November 2018

John J. Benedetto
John J. Benedetto*
Affiliation:
University of Maryland, College Park, Maryland
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In this paper we develop a natural notion of continuous pseudo-measure and study the Stieltjes integral with respect to a given pseudo-measure. The common feature to these two topics is the essential appearance in both of integrals having the form

Such integrals come about naturally when one defines the energy of distributions other than measures [6]. The reasons to study continuous pseudo-measures are to find properties analogous with those of continuous measures, and to discover more about the structure of pseudo-measures because of their importance in harmonic analysis, and particularly in spectral synthesis (e.g., [4; 15]). The Stieltjes integral with respect to a pseudo-measure is studied because of its intimate relation with spectral synthesis (e.g., §5); the key observations on this matter were initially made by Beurling [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 985 - 1001
Copyright
Copyright © Canadian Mathematical Society 1974

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