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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



A remark on the reproducing kernel thesis for Hankel operators

Author: S. Treil
Original publication: Algebra i Analiz, tom 26 (2014), nomer 3.
Journal: St. Petersburg Math. J. 26 (2015), 479-485
MSC (2010): Primary 47B35
Published electronically: March 20, 2015
MathSciNet review: 3289181
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Abstract | References | Similar Articles | Additional Information

Abstract: A simple proof is given of the so-called reproducing kernel thesis for Hankel operators.

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

  • 1. F. F. Bonsall, Boundedness of Hankel matrices, J. London Math. Soc. (2) 29 (1984), no. 2, 289-300. MR 744100 (85f:47030)
  • 2. B. Jacob, J. Partington, and S. Pott, Weighted interpolation in Paley-Wiener spaces and finite-time controllability, J. Funct. Anal. 259 (2010), no. 9, 2424-2436. MR 2674120 (2011g:93012)
  • 3. F. Nazarov, G. Pisier, S. Treil, and A. Volberg, Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts, J. Reine Angew. Math. 542 (2002), 147-171. MR 1880830 (2002m:47038)
  • 4. N. K. Nikol'skiĭ, Treatise on the shift operator, Spectral Function Theory, Grundlehren Math. Wiss., Bd. 273, Springer-Verlag, Berlin, 1986. MR 827223 (87i:47042)
  • 5. S. Petermichl, S. Treil, and B. Wick, Carleson potentials and the reproducing kernel thesis for embedding theorems, Illinois J. Math. 51 (2007), no. 4, 1249-1263. MR 2417425 (2009b:32008)
  • 6. S. Treil, Hankel operators, embedding theorems and bases of coinvariant subspaces of the multiple shift operator, Algebra i Analiz 1 (1989), no. 6, 200-234; English transl., Leningrad Math. J. 1 (1990), no. 6, 1515-1548. MR 1047967 (91f:47014)

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Additional Information

S. Treil
Affiliation: Department of Mathematics, Brown University, 151 Thayer Str./Box 1917, Providence, Rhode Island 02912

Keywords: Hankel operator, reproducing kernel thesis, Bonsall's theorem, Uchiyama's lemma
Received by editor(s): October 10, 2013
Published electronically: March 20, 2015
Additional Notes: This material is based on the work supported by the National Science Foundation under the grant DMS-0800876. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation
Article copyright: © Copyright 2015 American Mathematical Society

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