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Functional analysis proofs of Abel's theorems
Author(s):
M.
T.
Karaev
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2327-2329.
MSC (2000):
Primary 47A15
Posted:
February 13, 2004
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Abstract:
We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.
References:
-
- 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
Email:
garayev@fef.sdu.edu.tr
DOI:
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
Posted:
February 13, 2004
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2004,
American Mathematical Society
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