Pick interpolation in several variables
Author:
Ryan Hamilton
Journal:
Proc. Amer. Math. Soc. 141 (2013), 20972103
MSC (2010):
Primary 47A57; Secondary 30E05, 46E22
Published electronically:
January 30, 2013
MathSciNet review:
3034435
Fulltext PDF
Abstract 
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Additional Information
Abstract: We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in .
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 M.B. Abrahamse, The Pick interpolation theorem for finitely connected domains, Michigan Math. J. 26 (1979), 195203. MR 532320 (80j:30052)
 2.
 J. Agler and J.E. McCarthy, NevanlinnaPick interpolation on the bidisk, J. Reine Angew. Math. 506 (1999), 191204. MR 1665697 (2000a:47034)
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 H. Bercovici, The algebra of multiplication operators on Bergman spaces, Arch. Math. (Basel) 48 (1987), 165175. MR 878428 (88e:47057)
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 S.G. Krantz, Function theory of several complex variables, The Wadsworth & Brooks/Cole Mathematics Series, Second Edition, Pacific Grove, CA, 1992. MR 1162310 (93c:32001)
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 S. McCullough, NevanlinnaPick type interpolation in a dual algebra, J. Funct. Anal. 135 (1996), No. 1, 93131. MR 1367626 (96j:47013)
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 B. Prunaru, A factorization theorem for multiplier algebras of reproducing kernel Hilbert spaces, Canadian Math. Bull., to appear.
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Additional Information
Ryan Hamilton
Affiliation:
Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L–3G1, Canada
Email:
rhamilto@uwaterloo.ca
DOI:
http://dx.doi.org/10.1090/S000299392013115716
Keywords:
Pick interpolation,
reproducing kernel,
dual algebras
Received by editor(s):
October 5, 2011
Published electronically:
January 30, 2013
Additional Notes:
This work was partially supported by an NSERC graduate scholarship
Communicated by:
Richard Rochberg
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
