The peak sets of $A^{m}$
Authors:
B. A. Taylor and D. L. Williams
Journal:
Proc. Amer. Math. Soc. 24 (1970), 604-606
MSC:
Primary 30.70
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255828-9
MathSciNet review:
0255828
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let $A$ denote the algebra of functions analytic for $|z| < 1$ and continuous for $|z| \leqq 1$. For $m = 1,2, \cdots ,$, let ${A^m}$ be the algebra of functions $f$ such that $f,fâ, \cdots ,{f^{(m)}} \in A$; and let ${A^\infty } = \cap _{m = 1}^\infty {A^m}$. We show that the peak sets of ${A^m},1 \leqq m \leqq \infty$, are the finite subsets of $\{ |z| = 1\}$.
- Lennart Carleson, Sets of uniqueness for functions regular in the unit circle, Acta Math. 87 (1952), 325â345. MR 50011, DOI https://doi.org/10.1007/BF02392289
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1962. MR 0133008
- W. P. Novinger, Holomorphic functions with infinitely differentiable boundary values, Illinois J. Math. 15 (1971), 80â90. MR 269861
- Walter Rudin, Boundary values of continuous analytic functions, Proc. Amer. Math. Soc. 7 (1956), 808â811. MR 81948, DOI https://doi.org/10.1090/S0002-9939-1956-0081948-0
- B. A. Taylor and D. L. Williams, Ideals in rings of analytic functions with smooth boundary values, Canadian J. Math. 22 (1970), 1266â1283. MR 273024, DOI https://doi.org/10.4153/CJM-1970-143-x
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.70
Retrieve articles in all journals with MSC: 30.70
Additional Information
Keywords:
Algebra of analytic functions,
boundary values of analytic functions,
peak set,
interpolation
Article copyright:
© Copyright 1970
American Mathematical Society