Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



When is $ \mu \ast L\,\sb{1}$ closed?

Author: I. Glicksberg
Journal: Trans. Amer. Math. Soc. 160 (1971), 419-425
MSC: Primary 42.56; Secondary 46.00
MathSciNet review: 0288523
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a finite measure $ \mu $ on a locally compact abelian group, we partially answer the question of when $ \mu \ast {L_1}$ is closed in $ {L_1}$.

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

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [2] Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387
  • [3] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42.56, 46.00

Retrieve articles in all journals with MSC: 42.56, 46.00

Additional Information

Keywords: Locally compact abelian groups, convolve, Fourier transform
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society