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Niveau: Supérieur, Doctorat, Bac+8

Bases of reproducing kernels in model spaces EMMANUEL FRICAIN Abstract This paper deals with geometric properties of sequences of reproducing kernels related to invariant subspaces of the backward shift operator in the Hardy space H2. Let ? = (?n)n>1 ? D, ? be an inner function in H∞(L(E)), where E is a finite dimensional Hilbert space, and (en)n>1 a sequence of vectors in E. Then we give a criterion for the vector valued reproducing kernels (k?(., ?n)en)n>1 to be a Riesz basis for K? := H2(E) ?H2(E). Using this criterion, we extend to the vector valued case some basic facts that are well-known for the scalar valued reproducing kernels. Moreover, we study the stability problem, that is, given a Riesz basis (k?(., ?n))n>1, we characterize its perturbations (k?(., µn))n>1 that preserve the Riesz basis property. For the case of asymptotically orthonormal sequences, we give an effective upper bound for uniform perturbations preserving stability and compare our result with Kadecˇ's 1/4-theorem. 1 Introduction This paper is devoted to geometric properties of sequences of reproducing kernels in Hardy spaces. These properties are of interest for several reasons.

Bases of reproducing kernels in model spaces EMMANUEL FRICAIN Abstract This paper deals with geometric properties of sequences of reproducing kernels related to invariant subspaces of the backward shift operator in the Hardy space H2. Let ? = (?n)n>1 ? D, ? be an inner function in H∞(L(E)), where E is a finite dimensional Hilbert space, and (en)n>1 a sequence of vectors in E. Then we give a criterion for the vector valued reproducing kernels (k?(., ?n)en)n>1 to be a Riesz basis for K? := H2(E) ?H2(E). Using this criterion, we extend to the vector valued case some basic facts that are well-known for the scalar valued reproducing kernels. Moreover, we study the stability problem, that is, given a Riesz basis (k?(., ?n))n>1, we characterize its perturbations (k?(., µn))n>1 that preserve the Riesz basis property. For the case of asymptotically orthonormal sequences, we give an effective upper bound for uniform perturbations preserving stability and compare our result with Kadecˇ's 1/4-theorem. 1 Introduction This paper is devoted to geometric properties of sequences of reproducing kernels in Hardy spaces. These properties are of interest for several reasons.

- stability properties
- operator ?
- vector valued
- reproducing kernels
- perturbation
- perturbations preserving stability
- hilbert space
- valued reproducing
- all ? ?

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Published by | mijec |

Reads | 33 |

Language | English |

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