## 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. |

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### 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 backward shift ball of H belongs to H(b bounded operator Branges and Rovnyak Caratheodory's theorem Cauchy integral Chapter characterization closed graph theorem complementary space conditions are equivalent constant contained contractively convergence corona pair denote dense in 7i(b desired conclusion disk algebra eigenvalue exposed point extreme point form a corona function g function in H2 function in W(6 Hardy space Helson-Szego weight Hence Hilbert space holomorphic implies inequality inner function inner product invariant subspaces isometry of H2 Julia's lemma kernel function limit at z0 linear Lotto Math measure on dD Mobius transformation modulus multiplier of H(b nonextreme nontangential limit noted operator on H2 Operator Theory outer function partial isometry point of dD Poisson integral polynomial preceding proof proposition range right side rigid functions sense of Caratheodory singular component stays bounded Suppose tends nontangentially Toeplitz operators unit ball unit disk unit norm vector