Inner multipliers and Rudin type invariant subspaces

Chattopadhyay, Arup; Das, B. Krishna; Sarkar, Jaydeb

doi:10.14232/actasm-015-773-y

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2017

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“…This question was asked by Rudin in his book [4, p.78] and it is still open. Recently, for n = 2, two types of important invariant subspaces known as inner-sequence based invariant subspaces and invariant subspaces generated by two inner functions have been extensively studied by various authors in different context(see [6,9,8,7,11,12]). In this paper, inspired from these studies, we define two new types of invariant subspaces of H 2 (D n ) by considering a larger class of functions than inner functions.…”

Section: Introductionmentioning

confidence: 99%

Two Types of Invariant Subspaces in the Polydisc

Koca

2017

Results Math

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Abstract. It is known that the structure of invariant subspaces of the Hardy space H 2 (D n ) on the polydisc D n is very complicated; hence, we need good examples help us to understand the structure of invariant subspaces of H 2 (D n ). In this paper, we define two types of invariant subspaces of H 2 (D n ). Then, we give a characterization of these types invariant subspaces in view of the Beurling-Lax-Halmos Theorem. Unitary equivalence is also studied in this paper.

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Section: Introductionmentioning

confidence: 99%