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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: 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, vol. 1, Cambridge University Press, Cambridge, 1959. MR 21:6498
  • 2. R. E. Powell and S. M. Shah, Summability theory and applications, Van Nostrand Reinhold, London, 1972.
  • 3. E. Nordgren and P. Rosenthal, Boundary values of Berezin symbols, Nonselfadjoint Operators and Related Topics (Beer Sheva, 1992), Operator Theory: Advances and Applications, vol. 73, Birkhäuser, Basel, 1994, pp. 362-368. MR 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

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

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