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Let D n be the open unit polydisc in C n , n ≥ 1, and let H 2 (D n ) be the Hardy space over D n . For n ≥ 3, we show that if θ ∈ H ∞ (D n ) is an inner function, then the n-tuple of commuting operators (C z1 , . . . , C zn ) on the Beurling type quotient module Q θ is not essentially normal, whereRudin's quotient modules of H 2 (D 2 ) are also shown to be not essentially normal. We prove several results concerning boundary representations of C * -algebras corresponding to different classes of quotient modules including doubly commuting quotient modules and homogeneous quotient modules.2000 Mathematics Subject Classification. 47A13, 47A20, 47L25, 47L40, 46L05, 46L06.

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Rudin's submodules of H2(D2)

Cited by 4 publications

References 6 publications

Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

Ranks of fringe operators on finite Rudin type invariant subspaces

On quotient modules of H²(𝔻ⁿ): essential normality and boundary representations

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Rudin's submodules of H2(D2)

Cited by 4 publications

References 6 publications

Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

Ranks of fringe operators on finite Rudin type invariant subspaces

On quotient modules of H2(𝔻n): essential normality and boundary representations

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Product

Resources

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On quotient modules of H²(𝔻ⁿ): essential normality and boundary representations