Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

 

On the ideal of unconditionally convergent Fourier series in $L_{p} (G)$
HTML articles powered by AMS MathViewer

by Gregory F. Bachelis PDF
Proc. Amer. Math. Soc. 27 (1971), 309-312 Request permission

Abstract:

Let $G$ be a compact abelian group. We consider the ideal of functions in ${L_p}(G)$ with unconditionally convergent Fourier series in the ${L_p}$ norm. This ideal is shown to coincide with the “Derived algebra” of Helgason. A characterization of this ideal is given when $p$ is an even integer.
References
  • Gregory F. Bachelis, Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229–247. MR 244762
    • M. M. Day, Normed linear spaces, 2nd rev. ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
  • R. E. Edwards, Fourier series: a modern introduction. Vol. II, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1967. MR 0222538
  • Alexandre Grothendieck, RĂ©sultats nouveaux dans la thĂ©orie des opĂ©rations linĂ©aires. I, C. R. Acad. Sci. Paris 239 (1954), 577–579 (French). MR 66556
  • Alexandre Grothendieck, Produits tensoriels topologiques et espaces nuclĂ©aires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
    • G. H. Hardy and J. E. Littlewood, A problem concerning majorants of Fourier series, Quart. J. Math. 6 (1935), 304-315.
  • S. Helgason, Multipliers of Banach algebras, Ann. of Math. (2) 64 (1956), 240–254. MR 82075, DOI 10.2307/1969971
  • Irving Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689–701. MR 25452, DOI 10.2307/1969052
  • Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.56, 46.00
  • Retrieve articles in all journals with MSC: 42.56, 46.00
Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 309-312
  • MSC: Primary 42.56; Secondary 46.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0271640-X
  • MathSciNet review: 0271640