We discuss linear equations whose coefficients are bounded composition operators on the Hardy space over the unit disk. Some connections between those equations, Pick interpolation and de Branges-Rovnyak spaces are studied in detail.
References
M. T. Jury, Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators, Proc. Amer. Math. Soc. 135 (2007), 3669–3675. MR2336583 10.1090/S0002-9939-07-08931-9M. T. Jury, Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators, Proc. Amer. Math. Soc. 135 (2007), 3669–3675. MR2336583 10.1090/S0002-9939-07-08931-9
D. Sarason, Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Notes in the Mathematical Sciences, 10, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1994. MR1289670D. Sarason, Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Notes in the Mathematical Sciences, 10, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1994. MR1289670
