Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Linear projections which implement balayage in Fourier transforms
HTML articles powered by AMS MathViewer

by George S. Shapiro PDF
Proc. Amer. Math. Soc. 61 (1976), 295-299 Request permission

Abstract:

Let $\Lambda$ be a closed and discrete or compact subset of a second countable ${\text {LCA}}$ group $G$ and $E$ a subset of the dual group. Balayage is said to be possible for $(\Lambda ,\;E)$ if for every finite measure $\mu$ on $G$ there is some measure $\nu$ on $\Lambda$ whose Fourier transform, $\hat \nu$, agrees on $E$ with $\hat \mu$. If balayage is assumed possible just when $\mu$ is a point measure (with the norms of all the measures $\nu$ bounded by some constant), then there is a bounded linear projection, ${B_\Lambda }$, from the measures on $G$ onto those on $\Lambda$ with ${({B_\Lambda }\mu )^ \wedge } = \hat \mu$ on $E$. An application is made to balayage in product groups.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A25
  • Retrieve articles in all journals with MSC: 43A25
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 295-299
  • MSC: Primary 43A25
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0427957-3
  • MathSciNet review: 0427957