A class of $P^t(d\mu )$ spaces whose point evaluations vary with $t$
HTML articles powered by AMS MathViewer
- by John Akeroyd and Elias G. Saleeby PDF
- Proc. Amer. Math. Soc. 127 (1999), 537-542 Request permission
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
- John Akeroyd, An extension of Szegő’s theorem. II, Indiana Univ. Math. J. 45 (1996), no. 1, 241–252. MR 1406692, DOI 10.1512/iumj.1996.45.1195
- Thomas L. Kriete III, Cosubnormal dilation semigroups on Bergman spaces, J. Operator Theory 17 (1987), no. 2, 191–200. MR 887217
- Thomas L. Kriete III and Henry Crawford Rhaly Jr., Translation semigroups on reproducing kernel Hilbert spaces, J. Operator Theory 17 (1987), no. 1, 33–83. MR 873462
- James E. Thomson, Approximation in the mean by polynomials, Ann. of Math. (2) 133 (1991), no. 3, 477–507. MR 1109351, DOI 10.2307/2944317
- James E. Thomson, Bounded point evaluations and polynomial approximation, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1757–1761. MR 1242106, DOI 10.1090/S0002-9939-1995-1242106-1
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
- Received by editor(s): June 2, 1997
- Communicated by: Theodore W. Gamelin
- © Copyright 1999 American Mathematical Society
- 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
Dedicated: Dedicated to Richard H. Akeroyd