Abstract
A general class of strictly contractive block matrix valued functions g(ζ) = [gij (ζ)], i,j = 1,…,k, whose block entries gij are completely specified for j < i+τ (i.e., for gij below the τ’th block diagonal of g) and partially specified for j = i + τ (i.e., for gij on the τ’th block diagonal of g) is analyzed. Necessary and sufficient conditions for this class of “interpolants” to be nonempty are deduced. A linear fractional description of this class is then obtained and used to establish a maximum entropy principle. In particular it is shown that when this class is nonempty, then it contains exactly one interpolant which achieves the maximum entropy. This maximum entropy interpolant is also characterized as the “band” interpolant.
To Moshe Livšic, the founding father of the theory of Characteristic Operator Functions, on the occasion of his seventieth birthday, with admiration and affection.
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© 1988 Birkhäuser Verlag Basel
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Dym, H., Gohberg, I. (1988). A New Class of Contractive Interpolants and Maximum Entropy Principles. In: Gohberg, I. (eds) Topics in Operator Theory and Interpolation. Operator Theory: Advances and Applications, vol 29. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9162-2_5
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DOI: https://doi.org/10.1007/978-3-0348-9162-2_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-1960-1
Online ISBN: 978-3-0348-9162-2
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