Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Pick interpolation in several variables

Author: Ryan Hamilton
Journal: Proc. Amer. Math. Soc. 141 (2013), 2097-2103
MSC (2010): Primary 47A57; Secondary 30E05, 46E22
Published electronically: January 30, 2013
MathSciNet review: 3034435
Full-text PDF

Abstract | References | Similar Articles | 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 $ \mathbb{C}^d$.

References [Enhancements On Off] (What's this?)

  • 1. M.B. Abrahamse, The Pick interpolation theorem for finitely connected domains, Michigan Math. J. 26 (1979), 195-203. MR 532320 (80j:30052)
  • 2. J. Agler and J.E. McCarthy, Nevanlinna-Pick interpolation on the bidisk, J. Reine Angew. Math. 506 (1999), 191-204. MR 1665697 (2000a:47034)
  • 3. J. Agler and J.E. McCarthy, Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics 44, Amer. Math. Soc., Providence, RI, 2002. MR 1882259 (2003b:47001)
  • 4. H. Bercovici, The algebra of multiplication operators on Bergman spaces, Arch. Math. (Basel) 48 (1987), 165-175. MR 878428 (88e:47057)
  • 5. H. Bercovici, C. Foiaş, and C. Pearcy, Dual algebras with applications to invariant subspaces and dilation theory, CBMS Regional Conference Series in Mathematics, 56, Amer. Math. Soc., Providence, RI, 1985. MR 787041 (87g:47091)
  • 6. H. Bercovici and D. Westwood, The factorization of functions in the polydisc, Houston J. Math. 18 (1992), No. 1, 1-6. MR 1159434 (93b:32006)
  • 7. B.J. Cole, K. Lewis, and J. Wermer, Pick conditions on a uniform algebra and von Neumann inequalities, J. Funct. Anal. 107 (1992), 235-254. MR 1172022 (93e:46059)
  • 8. K.R. Davidson and R. Hamilton, Nevanlinna-Pick interpolation and factorization of linear functionals, Integral Equations Operator Theory 70 (2011), No. 1, 125-149. MR 2786738 (2012e:47045)
  • 9. R.G. Douglas and J. Sarkar, Some remarks on the Toeplitz corona problem, Hilbert spaces of analytic functions, CRM Proc. Lecture Notes, 51, 81-89, Amer. Math. Soc., Providence, RI, 2010. MR 2648868 (2011i:46051)
  • 10. 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)
  • 11. S. McCullough, Nevanlinna-Pick type interpolation in a dual algebra, J. Funct. Anal. 135 (1996), No. 1, 93-131. MR 1367626 (96j:47013)
  • 12. B. Prunaru, A factorization theorem for multiplier algebras of reproducing kernel Hilbert spaces, Canadian Math. Bull., to appear.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47A57, 30E05, 46E22

Retrieve articles in all journals with MSC (2010): 47A57, 30E05, 46E22

Additional Information

Ryan Hamilton
Affiliation: Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L–3G1, Canada

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.

American Mathematical Society