Journal of the Mathematical Society of Japan

Wandering subspaces and the Beurling type theorem, III

Kei-Ji IZUCHI, Kou-Hei IZUCHI, and Yuko IZUCHI

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Let $H^2(D^2)$ be the Hardy space over the bidisk. Let $\{\varphi_n(z)\}_{n \geq 0}$ and $\{\psi_n(w)\}_{n \geq 0}$ be sequences of one variable inner functions satisfying some additinal conditions. Associated with them, we have a Rudin type invariant subspace $\mathcal{M}$ of $H^2(D^2)$. We study the Beurling type theorem for the fringe operator $F_w$ on $\mathcal{M} \ominus z \mathcal{M}$.

Article information

J. Math. Soc. Japan, Volume 64, Number 2 (2012), 627-658.

First available in Project Euclid: 26 April 2012

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Zentralblatt MATH identifier

Primary: 47A15: Invariant subspaces [See also 47A46]
Secondary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Beurling type theorem wandering subspace invariant subspace fringe operator


IZUCHI, Kei-Ji; IZUCHI, Kou-Hei; IZUCHI, Yuko. Wandering subspaces and the Beurling type theorem, III. J. Math. Soc. Japan 64 (2012), no. 2, 627--658. doi:10.2969/jmsj/06420627.

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