Uniform algebras generated by holomorphic and pluriharmonic functions
Author:
Alexander J. Izzo
Journal:
Trans. Amer. Math. Soc. 339 (1993), 835847
MSC:
Primary 46J15; Secondary 32E25, 46E15
MathSciNet review:
1139494
Fulltext PDF Free Access
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Abstract: It is shown that if are pluriharmonic on (the open unit ball in and on , and the matrix is invertible at every point of , then the normclosed algebra generated by the ball algebra and is equal to . Extensions of this result to more general strictly pseudoconvex domains are also presented.
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 L. Hörmander, An introduction to complex analysis in several variables, 2nd ed., NorthHolland, 1979.
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 R. M. Range and Y. T. Sui, Uniform estimates for the equation on domains with piecewise smooth strictly pseudoconvex boundaries, Math. Ann. 206 (1973), 325354. MR 0338450 (49:3214)
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 W. Rudin, Function theory in the unit ball of , SpringerVerlag, New York, 1980. MR 601594 (82i:32002)
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 E. L. Stout, The theory of uniform algebras, Bogden & Quigley, New York, 1971. MR 0423083 (54:11066)
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 B. M. Weinstock, Zerosets of continuous holomorphic functions on the boundary of a strongly pseudoconvex domain, J. London Math. Soc. 18 (1978), 484488. MR 518233 (80e:32010)
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 J. Wermer, Polynomially convex disks, Math. Ann. 158 (1965), 610. MR 0174968 (30:5158)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199311394946
PII:
S 00029947(1993)11394946
Article copyright:
© Copyright 1993
American Mathematical Society
