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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Functional analysis proofs of Abel's theorems


Author: M. T. Karaev
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2327-2329
MSC (2000): Primary 47A15
Published electronically: February 13, 2004
MathSciNet review: 2052409
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Abstract | References | Similar Articles | Additional Information

Abstract: We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.


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

  • 1. A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776 (21 #6498)
  • 2. R. E. Powell and S. M. Shah, Summability theory and applications, Van Nostrand Reinhold, London, 1972.
  • 3. Eric Nordgren and Peter Rosenthal, Boundary values of Berezin symbols, Nonselfadjoint operators and related topics (Beer Sheva, 1992) Oper. Theory Adv. Appl., vol. 73, Birkhäuser, Basel, 1994, pp. 362–368. MR 1320554 (96b:46036)

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Additional Information

M. T. Karaev
Affiliation: Institute for Mathematics and Mechanics, Azerbaijanian National Academy of Sciences, F.Agaev, 9, 370141 Baku, Azerbaijan
Address at time of publication: Suleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, 32260 Isparta, Turkey
Email: garayev@fef.sdu.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07354-X
PII: S 0002-9939(04)07354-X
Keywords: Abel convergent, Berezin symbol, diagonal operator
Received by editor(s): March 3, 2003
Received by editor(s) in revised form: April 28, 2003
Published electronically: February 13, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society