Bohr’s inequality for uniform algebras

Paulsen, Vern; Singh, Dinesh

doi:10.1090/S0002-9939-04-07553-7

Bohr’s inequality for uniform algebras
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by Vern I. Paulsen and Dinesh Singh PDF

Proc. Amer. Math. Soc. 132 (2004), 3577-3579 Request permission

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

Lev Aizenberg, Multidimensional analogues of Bohr’s theorem on power series, Proc. Amer. Math. Soc. 128 (2000), no. 4, 1147–1155. MR 1636918, DOI 10.1090/S0002-9939-99-05084-4
Harold P. Boas and Dmitry Khavinson, Bohr’s power series theorem in several variables, Proc. Amer. Math. Soc. 125 (1997), no. 10, 2975–2979. MR 1443371, DOI 10.1090/S0002-9939-97-04270-6
Harold P. Boas, Majorant series, J. Korean Math. Soc. 37 (2000), no. 2, 321–337. Several complex variables (Seoul, 1998). MR 1775963
H. Bohr, A theorem concerning power series, Proc. London Math. Soc. 2(13)1914, 1-5.
P. G. Dixon, Banach algebras satisfying the non-unital von Neumann inequality, Bull. London Math. Soc. 27 (1995), no. 4, 359–362. MR 1335287, DOI 10.1112/blms/27.4.359
Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
Vern I. Paulsen, Gelu Popescu, and Dinesh Singh, On Bohr’s inequality, Proc. London Math. Soc. (3) 85 (2002), no. 2, 493–512. MR 1912059, DOI 10.1112/S0024611502013692
S. Sidon, Uber einen satz von Herrn Bohr, Math. Zietschrift, (26)1927, 731-732.