A Note on Rudin’s Pathological Submodule in $$H^{2}({\mathbb {D}}^2)$$ H 2 ( D 2 )

A Note on Rudin’s Pathological Submodule in $$H^{2}({\mathbb {D}}^2)$$ H 2 ( D 2 ) In Rudin (Function theory in polydiscs, Benjamin, New York 1969) constructed a submodule in $$H^{2}({\mathbb {D}}^2)$$ H 2 ( D 2 ) that contains no nontrivial bounded functions. This paper shows that this type of submodules is Hilbert–Schmidt by selecting a suitable power sequence. In an attempt to generalized Rudin’s submodules, the paper defines zero-based submodule and makes a preliminary study about its Hilbert–Schmidtness. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Integral Equations and Operator Theory Springer Journals

A Note on Rudin’s Pathological Submodule in $$H^{2}({\mathbb {D}}^2)$$ H 2 ( D 2 )

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Springer International Publishing
Copyright © 2017 by Springer International Publishing
Mathematics; Analysis
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