TY - CHAP

T1 - Rational functions

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Sabadini, Irene

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In classical Schur analysis, operator-valued functions appear naturally in a number of different settings, of which we mention: 1. The characteristic operator function, when the imaginary part of the operator is not of finite rank (but possibly trace class, or of Hilbert–Schmidt class). See for instance [110, 111, 242]. 2. The time-varying case, when the complex numbers are replaced by diagonal operators. See [40, 161, 162, 163]. 3. Interpolation in the Hardy space of the polydisk. One can reduce the problem to an operator-valued problem in one variable. The values are then assumed to be Hilbert-Schmidt operators. See [23, 24].

AB - In classical Schur analysis, operator-valued functions appear naturally in a number of different settings, of which we mention: 1. The characteristic operator function, when the imaginary part of the operator is not of finite rank (but possibly trace class, or of Hilbert–Schmidt class). See for instance [110, 111, 242]. 2. The time-varying case, when the complex numbers are replaced by diagonal operators. See [40, 161, 162, 163]. 3. Interpolation in the Hardy space of the polydisk. One can reduce the problem to an operator-valued problem in one variable. The values are then assumed to be Hilbert-Schmidt operators. See [23, 24].

UR - http://www.scopus.com/inward/record.url?scp=85006253708&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42514-6_2

DO - 10.1007/978-3-319-42514-6_2

M3 - Chapter

AN - SCOPUS:85006253708

T3 - Operator Theory: Advances and Applications

SP - 23

EP - 35

BT - Operator Theory

PB - Springer International Publishing

ER -