A construction of Hilbert spaces of analytic functions

Author:
William W. Hastings

Journal:
Proc. Amer. Math. Soc. **74** (1979), 295-298

MSC:
Primary 46E20; Secondary 47B20

MathSciNet review:
524303

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A simple technique is presented for constructing a measure from a given measure so that has certain properties. Here, is the closure in of the rational functions with poles off *K*, a compact set containing the support of . A typical example shows that there exists a measure mutually absolutely continuous with area measure on the unit disk such that (principal branch) is an element of , while each point of the open disk except on the negative real axis is an analytic bounded point evaluation for .

**[1]**Joseph Bram,*Subnormal operators*, Duke Math. J.**22**(1955), 75–94. MR**0068129****[2]**W. S. Clary,*Quasi-similarity and subnormal operators*, Dissertation, Univ. of Michigan, 1973.**[3]**M. J. Cowen and R. G. Douglas,*Complex geometry and operator theory*, Bull. Amer. Math. Soc.**83**(1977), no. 1, 131–133. MR**0500206**, 10.1090/S0002-9904-1977-14215-8**[4]**Theodore W. Gamelin,*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR**0410387****[5]**Thomas Kriete,*The growth of point evaluation functionals in certain**spaces*(preprint).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46E20,
47B20

Retrieve articles in all journals with MSC: 46E20, 47B20

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0524303-4

Article copyright:
© Copyright 1979
American Mathematical Society