Sub-Hardy Hilbert Spaces in the Unit DiskThis up-to-date account brings together results previously scattered throughout the literature as well as new material in the area of function theory. The focus is on describing some of what has been learned thus far about the structure of the de Branges-Rovnyak spaces and their function-theoretic connections. |
Contents
Hilbert Spaces Inside Hilbert Spaces | 1 |
Hilbert Spaces Inside H2 | 9 |
Cauchy Integral Representations | 15 |
Copyright | |
11 other sections not shown
Common terms and phrases
absolutely continuous adjoint angular derivative assume b(zo backward shift ball of H belongs to H(b bounded operator Branges and Rovnyak Branges-Rovnyak spaces Carathéodory's theorem Cauchy integral Chapter characterization closed graph theorem complementary space conditions are equivalent convergence corona pair criterion denote dense in H(b desired conclusion disk algebra eigenvalue equality H(b exposed point extreme point form a corona function g function in H(b h in H(b Hence Hilbert space Ho(b holds holomorphic implies inequality inner function inner product invariant subspaces invertible isometry of H(b Julia's lemma kernel function L²(p Math measure µ Möbius transformation modulus multiplier of H(b nonextreme nontangential limit operator on H² Operator Theory outer function partial isometry Poisson integral polynomial preceding proof rigid functions Sarason sense of Carathéodory spaces H(b tends nontangentially TF/F Toeplitz operators unit ball vector y₁