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Bohr's inequality for uniform algebras
Author(s):
Vern
I.
Paulsen;
Dinesh
Singh
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3577-3579.
MSC (2000):
Primary 46J10, 46J15;
Secondary 30B10
Posted:
July 22, 2004
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Abstract:
We prove a uniform algebra analogue of a classical inequality of Bohr's concerning Fourier coefficients of bounded holomorphic functions. The classical inequality follows trivially.
References:
-
- 1.
- L. Aizenberg, Multidimensional analogues of Bohr's theorem on power series, Proc. Amer. Math. Soc. 128(2000), 1147-1155. MR 1636918 (2000i:32001)
- 2.
- H. P. Boas and D. Khavinson, Bohr's power series theorem in several variables, Proc. Amer. Math. Soc. 125(1997), 2975-2979. MR 1443371 (98i:32002)
- 3.
- H. P. Boas, Majorant Series, J. Korean Math. Soc. 2(37)2000, 321-337. MR 1775963 (2001j:32001)
- 4.
- H. Bohr, A theorem concerning power series, Proc. London Math. Soc. 2(13)1914, 1-5.
- 5.
- P. G. Dixon, Banach algebras satisfying the non-unital von Neumann inequality, Bull. London Math. Soc. (27)1995, 359-362. MR 1335287 (96e:46061)
- 6.
- T. W. Gamelin, Uniform Algebras, Prentice Hall, 1969. MR 0410387 (53:14137)
- 7.
- V. I. Paulsen, G. Popescu and D. Singh, On Bohr's inequality, Proc. London Math. Soc. 3(85)2002, 493-512. MR 1912059 (2003h:47025)
- 8.
- S. Sidon, Uber einen satz von Herrn Bohr, Math. Zietschrift, (26)1927, 731-732.
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Additional Information:
Vern
I.
Paulsen
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
vern@math.uh.edu
Dinesh
Singh
Affiliation:
Department of Mathematics, University of Delhi, Delhi 110007, India
Email:
dinesh_singh@hotmail.com
DOI:
10.1090/S0002-9939-04-07553-7
PII:
S 0002-9939(04)07553-7
Keywords:
Bohr's inequality,
uniform algebras.
Received by editor(s):
June 1, 2003
Posted:
July 22, 2004
Communicated by:
David R. Larson
Copyright of article:
Copyright
2004,
American Mathematical Society
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