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Bohr's power series theorem in several variables
Author(s):
Harold
P.
Boas;
Dmitry
Khavinson
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2975-2979.
MSC (1991):
Primary 32A05
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Abstract:
Generalizing a classical one-variable theorem of Bohr, we show that if an  -variable power series has modulus less than  in the unit polydisc, then the sum of the moduli of the terms is less than  in the polydisc of radius  .
References:
- 1.
- H. F. Bohnenblust and Einar Hille, On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), 600-622.
- 2.
- Harald Bohr, A theorem concerning power series, Proc. London Math. Soc. (2) 13 (1914), 1-5.
- 3.
- Seán Dineen and Richard M. Timoney, Absolute bases, tensor products and a theorem of Bohr, Studia Math. 94 (1989), 227-234. MR 91e:46006
- 4.
- -, On a problem of H. Bohr, Bull. Soc. Roy. Sci. Liège 60 (1991), no. 6, 401-404. MR 93e:46050
- 5.
- Jean-Pierre Kahane, Some random series of functions, second ed., Cambridge University Press, 1985. MR 87m:60119
- 6.
- Steven G. Krantz, Function theory of several complex variables, second ed., Wadsworth & Brooks/Cole, Pacific Grove, CA, 1992. MR 93c:32001
- 7.
- Anna Maria Mantero and Andrew Tonge, The Schur multiplication in tensor algebras, Studia Math. 68 (1980), no. 1, 1-24. MR 81k:46074
- 8.
- Walter Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 41:501
- 9.
- S. Sidon, Über einen Satz von Herrn Bohr, Math. Z. 26 (1927), 731-732.
- 10.
- M. Tomic, Sur un théorème de H. Bohr, Math. Scand. 11 (1962), 103-106. MR 31:316
- 11.
- N. Th. Varopoulos, On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory, J. Funct. Anal. 16 (1974), 83-100. MR 50:8116
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Additional Information:
Harold
P.
Boas
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843--3368
Email:
boas@math.tamu.edu
Dmitry
Khavinson
Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email:
dmitry@comp.uark.edu
DOI:
10.1090/S0002-9939-97-04270-6
PII:
S 0002-9939(97)04270-6
Received by editor(s):
May 8, 1996
Additional Notes:
The first author's research was supported in part by NSF grant number DMS 9500916 and in part at the Mathematical Sciences Research Institute by NSF grant number DMS 9022140.
Communicated by:
Theodore W. Gamelin
Copyright of article:
Copyright
1997,
American Mathematical Society
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