Overview
- Editors:
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I. Gohberg
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School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel
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Table of contents (6 chapters)
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- Joseph A. Ball, Israel Gohberg, Leiba Rodman
Pages 1-72
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- I. Gohberg, M. A. Kaashoek, A. C. M. Ran
Pages 73-108
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- I. Gohberg, M. A. Kaashoek
Pages 109-122
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- Joseph A. Ball, Nir Cohen, André C. M. Ran
Pages 123-173
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- Daniel Alpay, Israel Gohberg
Pages 175-222
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- Israel Gohberg, Sorin Rubinstein
Pages 223-247
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About this book
One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.
Editors and Affiliations
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School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel
I. Gohberg
