In Rudin (Function theory in polydiscs, Benjamin, New York 1969) constructed a submodule in $$H^{2}({\mathbb {D}}^2)$$H2(D2) that contains no nontrivial bounded functions. This paper shows that this type of submodules… Click to show full abstract
In Rudin (Function theory in polydiscs, Benjamin, New York 1969) constructed a submodule in $$H^{2}({\mathbb {D}}^2)$$H2(D2) 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.
Keywords:
rudin pathological;
rudin;
submodule mathbb;
note rudin;
submodule
Journal Title: Integral Equations and Operator Theory
Year Published: 2017
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Journal Title: Integral Equations and Operator Theory
Year Published: 2017
Link to full text (if available)
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recommendations!