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Aϕ-Invariant Subspaces on the Torus

Published online by Cambridge University Press:  20 November 2018

Keiji Izuchi  and
Yasuo Matsugu
Keiji Izuchi
Affiliation:
Department of Mathematics Niigata University Niigata950-21 Japan, e-mail: izuchi@scux.sc.niigata-u.ac.jp
Yasuo Matsugu
Affiliation:
Department of Mathematics Shinshu University Matsumoto 390 Japan, e-mail: ymatsugu@ripms.shinshu-u.ac.jp
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Abstract

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Generalizing the notion of invariant subspaces on the 2-dimensional torus ${{T}^{2}}$, we study the structure of ${{A}_{\phi }}$-invariant subspaces of ${{L}^{2}}({{T}^{2}})$. A complete description is given of ${{A}_{\phi }}$-invariant subspaces that satisfy conditions similar to those studied by Mandrekar, Nakazi, and Takahashi.

Keywords

32A3547A15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 1 , 01 February 1998 , pp. 99 - 133
Copyright
Copyright © Canadian Mathematical Society 1998

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