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Additional Material for the Book
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Interpolation and Sampling in Spaces of Analytic Functions
Publication Year: 2004
University Lecture Series, vol. 33
This page is maintained by the author
Department of Mathematical Sciences
Norwegian University of Science & Technology
N-7491 Trondheim, Norway
Email: Kristian Seip
Two updates on the bibliography of the book:
The preprint [BN02] (B. Bøe & A. Nicolau, "Interpolation by functions in the Bloch space") will appear in J. Analyse Math. ;
the preprint [Bø03] (B. Bøe, "An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernels") will appear in Proc. Amer. Math. Soc.
I would like to express my gratitude to the authors for their permission to include material from these still unpublished papers in the book.
There are two slight mistakes on page 28.
In the displayed formula on line 16, the definitions of B and C have been interchanged.
Also, in the last displayed formula on that same page, the n appearing in the entries of the matrix should instead be n+1.
References related to Parrott's lemma
I thank Vasily Vasyunin for pointing out the relevance of these papers.
C. Davis, W. M. Kahane, and H. F. Weinberger,
SIAM J. Numer. Anal. 19 (1982), no. 3, 445--469;
Yu. L. Shmul'yan and R. N. Yanovskaya,
Izv. Vyssh. Uchebn. Zaved. Mat. 1981, no. 7, 72--75;
Arsene and Gheondea,
J. Operator Theory 7 (1982), no. 1, 179--189;
I gave two references ([Par78] and [AgMc02]) for Parrott's lemma. Several other papers could have been cited. In particular, a beautiful explicit formula for the extension can be found in:Similar results appear in:and