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Zeros of functions with finite Dirichlet integral

Author(s): Stefan Richter; William T. Ross; Carl Sundberg
Journal: Proc. Amer. Math. Soc. 132 (2004), 2361-2365.
MSC (2000): Primary 30C15; Secondary 30C85
Posted: February 12, 2004
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Abstract: In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

References:

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T. Bagby, Quasi topologies and rational approximation, J. Functional Analysis 10 (1972), 259-268. MR 50:7535

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K. Bogdan, On the zeros of functions with finite Dirichlet integral, Kodai Math. J. 19 (1996), no. 1, 7-16. MR 96k:30005

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L. Carleson, On the zeros of functions with bounded Dirichlet integrals, Math. Z. 56 (1952), 289-295. MR 14:458e

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P. L. Duren, Theory of ${H}\sp{p}$ spaces, Academic Press, New York, 1970.MR 42:3552

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A. Nagel, W. Rudin, and J. Shapiro, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math. (2) 116 (1982), no. 2, 331-360.MR 84a:31002

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H. S. Shapiro and A. L. Shields, On the zeros of functions with finite Dirichlet integral and some related function spaces, Math. Z. 80 (1962), 217-229.MR 26:2617

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Additional Information:

Stefan Richter
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: richter@math.utk.edu

William T. Ross
Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
Email: wross@richmond.edu

Carl Sundberg
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: sundberg@math.utk.edu

DOI: 10.1090/S0002-9939-04-07361-7
PII: S 0002-9939(04)07361-7
Received by editor(s): October 22, 2002
Received by editor(s) in revised form: May 6, 2003
Posted: February 12, 2004
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2004, American Mathematical Society

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