Operator theory in the Hardy space over the bidisk. I

DOI10.1007/BF01200124zbMath0970.47016OpenAlexW2061852150MaRDI QIDQ1589663

Rongwei Yang, Ronald G. Douglas

Publication date: 12 October 2001

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01200124

zbMATH Keywords

Hardy space over the bidisksubmodulesuniversal model for the contractive analytic functionsvector valued Hardy space

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Canonical models for contractions and nonselfadjoint linear operators (47A45)

Related Items (28)

Defect operators, defect functions and defect indices for analytic submodules ⋮ Applications of Hilbert Module Approach to Multivariable Operator Theory ⋮ Properties of Beurling-type submodules via Agler decompositions ⋮ Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk ⋮ Ranks of backward shift invariant subspaces of the Hardy space over the bidisk ⋮ Properties of vector-valued submodules on the bidisk ⋮ A geometric approach to the compressed shift operator on the Hardy space over the bidisk ⋮ Dilation theory and analytic model theory for doubly commuting sequences of \(C_{\cdot 0}\)-contractions ⋮ Fredholm index of 3-tuple of restriction operators and the pair of fringe operators for submodules in \(H^2(\mathbb{D}^3)\) ⋮ Wandering subspaces and the Beurling type theorem. III ⋮ Mutually prime sequences of inner functions and the ranks of subspaces over the bidisk ⋮ Blaschke products and the rank of backward shift invariant subspaces over the bidisk ⋮ SPLITTING INVARIANT SUBSPACES IN THE HARDY SPACE OVER THE BIDISK ⋮ Tensor product of quotient Hilbert modules ⋮ Doubly commuting mixed invariant subspaces in the polydisc ⋮ Rudin's submodules of \(H^2(\mathbb{D}^2)\) ⋮ Operator theory in the Hardy space over the bidisk. III ⋮ A New Proof that Rudin’s Module is not Finitely Generated ⋮ Multiplication operators on the Bergman space via the Hardy space of the bidisk ⋮ The operator \(M_{z_1^n z_2^n}\) on subspaces of Bergman spaces over the biannulus ⋮ \(N_{\psi}\)-type quotient modules in \(H^2(\mathbb{D}^n)\) ⋮ Multiplicities, invariant subspaces and an additive formula ⋮ Beurling type theorem on the Bergman space via the Hardy space of the bidisk ⋮ The reducibility of compressed shifts on Beurling type quotient modules over the bidisk ⋮ Submodules of the Hardy module over the polydisc ⋮ Rank of a co-doubly commuting submodule is 2 ⋮ Hilbert polynomials and Arveson's curvature invariant. ⋮ Properties of compressed shifts on Beurling type quotient module of Hardy space over the bidisk

Cites Work

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• Beurling's theorem for the Bergman space
• The Validity of Beurling Theorems in Polydiscs
• Szego's Theorem on a Bidisc
• Rings with Topologies Induced by Spaces of Functions

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