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A class of $P^t(d\mu )$ spaces
whose point evaluations vary with $t$


Authors: John Akeroyd and Elias G. Saleeby
Journal: Proc. Amer. Math. Soc. 127 (1999), 537-542
MSC (1991): Primary 30E10, 46E15
DOI: https://doi.org/10.1090/S0002-9939-99-04617-1
MathSciNet review: 1473652
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Abstract | References | Similar Articles | Additional Information

Abstract: Extending an example given by T. Kriete, we develop a class of measures each of which consists of a measure on $\{z:\,|z|{}=1\}$ along with a series of weighted point masses in $\mathbf{D:=}\{z:\,|z|{}<1\}$. This class provides relatively simple examples of measures $\mu $ which have the property that the collection of analytic bounded point evaluations for $P^{t}(d\mu )$ varies with $t$. The first known measures with this property were recently constructed by J. Thomson.


References [Enhancements On Off] (What's this?)

  • 1. J. Akeroyd, An extension of Szegö's Theorem II, Indiana Univ. Math. J., Vol. 45, No. 1 (1996), 241-252. MR 97h:30055
  • 2. T. L. Kriete, Cosubnormal dilation semigroups on Bergman spaces, J. Operator Theory 17 (1987), 191-200. MR 88e:47041
  • 3. T. L. Kriete and H. C. Rhaly, Translation semigroups on reproducing kernel Hilbert spaces, J. Operator Theory 17 (1987), 33-83. MR 88e:47080
  • 4. J. Thomson, Approximation in the mean by polynomials, Ann. of Math. (2) 133 (1991), 477-507. MR 93g:47026
  • 5. J. Thomson, Bounded point evaluations and polynomial approximation, Proc. Amer. Math. Soc., Vol. 123, No. 6 (1995), 1757-1761.MR 95g:30051

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Additional Information

John Akeroyd
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: jakeroyd@comp.uark.edu

Elias G. Saleeby
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: esaleeby@comp.uark.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04617-1
Received by editor(s): June 2, 1997
Dedicated: Dedicated to Richard H. Akeroyd
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society

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