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Interpolating sequences in harmonically weighted Dirichlet spaces
Author:
António Serra
Journal:
Proc. Amer. Math. Soc. 131 (2003), 2809-2817
MSC (2000):
Primary 30E05; Secondary 46E20
Posted:
January 2, 2003
MathSciNet review:
1974338
Full-text PDF Free Access
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Abstract: We describe the interpolating sequences and weak interpolating sequences for the multiplier algebras of harmonically weighted Dirichlet spaces  when  is a finitely atomic measure.
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- William G. Bade and Philip C. Curtis, Jr.
The Wedderburn decomposition of commutative Banach algebras.
Amer. J. Math., 82:851-866, 1960. MR 23:A529
- 2.
- Lennart Carleson.
An interpolation problem for bounded analytic functions.
Amer. J. Math., 80:921-930, 1958. MR 22:8129
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- John B. Garnett.
Bounded analytic functions.
Academic Press, Inc. [Harcourt Brace Jovanovich Publishers], New York, 1981. MR 83g:30037
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- Kenneth Hoffman.
Banach spaces of analytic functions.
Dover Publications Inc., New York, 1988.
Reprint of the 1962 original. MR 92d:46066
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- Donald Marshall and Carl Sundberg.
Interpolating sequences for the multipliers of the Dirichlet space.
Preprint.
- 6.
- Stefan Richter.
A representation theorem for cyclic analytic two-isometries.
Trans. Amer. Math. Soc., 328(1):325-349, 1991. MR 92e:47052
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- Stefan Richter and Carl Sundberg.
A formula for the local Dirichlet integral.
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- Donald Sarason.
Doubly shift-invariant spaces in  .
J. Operator Theory, 16(1):75-97, 1986. MR 88d:47014b
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Local Dirichlet spaces as de Branges-Rovnyak spaces.
Proc. Amer. Math. Soc., 125(7):2133-2139, 1997. MR 98h:46023
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On some interpolation problems for analytic functions.
Amer. J. Math., 83:513-532, 1961. MR 24:A3280
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Additional Information
António Serra
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication:
Departamento de Matemática-IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Email:
aserra@math.ist.utl.pt
DOI:
http://dx.doi.org/10.1090/S0002-9939-03-06846-1
PII:
S 0002-9939(03)06846-1
Keywords:
Interpolating sequences,
weighted Dirichlet spaces
Received by editor(s):
May 3, 2001
Received by editor(s) in revised form:
April 3, 2002
Posted:
January 2, 2003
Additional Notes:
This work was fully supported by the PRAXIS XXI program, scholarship BD/11064/97, F.C.T., Lisbon, Portugal
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2003 American Mathematical Society
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