Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Interpolating sequences in harmonically weighted Dirichlet spaces

Author(s): António Serra
Journal: Proc. Amer. Math. Soc. 131 (2003), 2809-2817.
MSC (2000): Primary 30E05; Secondary 46E20
Posted: January 2, 2003
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: We describe the interpolating sequences and weak interpolating sequences for the multiplier algebras of harmonically weighted Dirichlet spaces $D(\mu)$ when $\mu$ is a finitely atomic measure.

References:

1.
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

3.
John B. Garnett.
Bounded analytic functions.
Academic Press, Inc. [Harcourt Brace Jovanovich Publishers], New York, 1981. MR 83g:30037

4.
Kenneth Hoffman.
Banach spaces of analytic functions.
Dover Publications Inc., New York, 1988.
Reprint of the 1962 original. MR 92d:46066

5.
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

7.
Stefan Richter and Carl Sundberg.
A formula for the local Dirichlet integral.
Michigan Math. J., 38(3):355-379, 1991. MR 92i:47035

8.
Donald Sarason.
Doubly shift-invariant spaces in ${H}\sp 2$.
J. Operator Theory, 16(1):75-97, 1986. MR 88d:47014b

9.
Donald Sarason.
Local Dirichlet spaces as de Branges-Rovnyak spaces.
Proc. Amer. Math. Soc., 125(7):2133-2139, 1997. MR 98h:46023

10.
H. S. Shapiro and A. L. Shields.
On some interpolation problems for analytic functions.
Amer. J. Math., 83:513-532, 1961. MR 24:A3280

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30E05, 46E20

Retrieve articles in all Journals with MSC (2000): 30E05, 46E20

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: 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
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google