Marinus A. Kaashoek Livres

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.

This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer’s research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia type results, matrix polynomials, and related areas in operator and matrix theory. Biographical material and Lerer's list of publications complete the volume.

This volume features a selection of papers in modern operator theory and its applications, primarily stemming from the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, from June 24–27, 2003. The workshop gathered 108 mathematicians, including PhD and postdoctoral students, from 22 countries. It included eight special sessions covering topics such as control theory, interpolation theory, inverse scattering, numerical estimates for operators, numerical treatment of integral equations, pseudodifferential operators, realizations and transformations of analytic functions and indefinite inner product spaces, and structured matrices. The program featured 19 plenary lectures and 78 shorter talks across four parallel sessions. This volume captures the diverse range of topics discussed at the workshop, including inverse scattering, numerical ranges, pseudodifferential operators, numerical analysis, multidimensional system theory, indefinite inner products, spectral factorization, and stationary processes. Additionally, the proceedings are dedicated to Israel Gohberg, president of the IWOTA steering committee, in honor of his 75th birthday, with all authors joining in this tribute.