Interpolating sequences and invariant subspaces of given index in the Bergman spaces.

DOI10.1515/crll.1996.477.13zbMath0895.46023OpenAlexW1596948246MaRDI QIDQ4888723

Haakan Hedenmalm, Kristian Seip, Stephan Richter

Publication date: 6 September 1998

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/153837

zbMATH Keywords

invariant subspaceindexweighted Bergmann spaceedge between interpolating and sampling sequencesgeneral Banach spaces of analytic functions on a bounded region

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of bounded analytic functions of one complex variable (30H05) Entire and meromorphic functions of one complex variable, and related topics (30D99)

Related Items (32)

A note concerning the index of the shift ⋮ Sampling and interpolation in large Bergman and Fock spaces ⋮ Weighted Bergman spaces: shift-invariant subspaces and input/state/output linear systems ⋮ Beurling's theorem for the Bergman space ⋮ Maximal invariant subspaces in the Bergman space ⋮ Wandering subspaces and the Beurling type theorem. I ⋮ Wandering subspaces and quasi-wandering subspaces in the Hardy-Sobolev spaces ⋮ Zero-based subspaces and quasi-invariant subspaces of the Bargmann-Fock space ⋮ Finite zero-based invariant subspaces of the shift operator on reproducing kernel spaces ⋮ Random weighted shifts ⋮ Sets of sampling and interpolation in Bergman spaces ⋮ Large Bergman spaces: Invertibility, cyclicity, and subspaces of arbitrary index. ⋮ Invariant subspaces of the harmonic Dirichlet space with large co-dimension ⋮ Wandering subspace property for homogeneous invariant subspaces ⋮ Some sufficient conditions for the division property of invariant subspaces in weighted Bergman spaces ⋮ Regular sets of sampling and interpolation in Bergman spaces ⋮ Bloch functions and asymptotic tail variance ⋮ Beurling's theorem and invariant subspaces for the shift on Hardy spaces ⋮ The majorization function and the index of invariant subspaces in the Bergman spaces. ⋮ Maximal invariant subspaces for a class of operators ⋮ A characteristic operator function for the class of \(n\)-hypercontractions ⋮ Beurling type theorem on the Hilbert space generated by a positive sequence ⋮ Maximal, minimal, and primary invariant subspaces ⋮ Quasi-wandering subspaces in the Bergman space ⋮ Invariant subspaces and reducing subspaces of weighted Bergman space over bidisk ⋮ Closed-range composition operators on \(\mathbb A^2\) ⋮ \(M_\varphi\)-type submodules over the bidisk ⋮ An expansive multiplier property for operator-valued Bergman inner functions ⋮ Wandering subspace property of the shift operator on a class of invariant subspaces of the weighted Bergman space \(L_a^2(dA_2)\) ⋮ Closed densely defined operators commuting with multiplications in a multiplier pair ⋮ Multiplicities, invariant subspaces and an additive formula ⋮ Linear graph transformations on spaces of analytic functions

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