# Additional Material for the Book

Interpolation and Sampling in Spaces of Analytic Functions
Kristian Seip
Publication Year: 2004
ISBN-10: 0-8218-3554-8
ISBN-13: 978-0-8218-3554-8
University Lecture Series, vol. 33

Contact information:

Kristian Seip
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I would like to express my gratitude to the authors for their permission to include material from these still unpublished papers in the book.

#### Two corrections

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;
MR0656462 (84b:47010).
• Yu. L. Shmul'yan and R. N. Yanovskaya,
Izv. Vyssh. Uchebn. Zaved. Mat. 1981, no. 7, 72--75;
MR0636919 (83e:47007)
• Arsene and Gheondea,
J. Operator Theory 7 (1982), no. 1, 179--189;
MR0650203 (83i:47010).
• 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