Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Linear projections which implement balayage in Fourier transforms

Author: George S. Shapiro
Journal: Proc. Amer. Math. Soc. 61 (1976), 295-299
MSC: Primary 43A25
MathSciNet review: 0427957
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A25

Retrieve articles in all journals with MSC: 43A25

Additional Information

Keywords: Balayage in Fourier transforms, point measures, measurable choice, analytic set, weak- <IMG WIDTH="15" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$^{\ast }$"> integral, bounded linear projection, balayage in product groups
Article copyright: © Copyright 1976 American Mathematical Society