Toeplitz operators in the commutant of a composition operator

Bruce Cload

Displaying similar documents to “Toeplitz operators in the commutant of a composition operator”

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

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Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk $^{N}$ or on the Segal-Bargmann space over $ℂ^{N}$ . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression $A_{n}$ of A to the linear span of the monomials $z_{1}^{k_{1}} . . . z_{N}^{k_{N}} : 0 \leq k_{j} \leq n$ . Unfortunately, in general the spectrum of $A_{n}$ does not mimic the spectrum...

Some density theorems for Toeplitz operators on Bergman spaces

Miroslav Engliš (1990)

Czechoslovak Mathematical Journal

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Toeplitz operators related to certain domains in $C^{n}$

J. Janas (1975)

Studia Mathematica

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Partial differential operators depending analytically on a parameter

Frank Mantlik (1991)

Annales de l'institut Fourier

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Let $P (λ, D) = \sum_{| α | \leq m} a_{α} (λ) D^{α}$ be a differential operator with constant coefficients $a_{α}$ depending analytically on a parameter $λ$ . Assume that the family ${$ P( $λ$ ,D) $}$ is of constant strength. We investigate the equation $P (λ, D) 𝔣_{λ} \equiv g_{λ}$ where $𝔤_{λ}$ is a given analytic function of $λ$ with values in some space of distributions and the solution $𝔣_{λ}$ is required to depend analytically on $λ$ , too. As a special case we obtain a regular fundamental solution of P( $λ$ ,D) which depends analytically on $λ$ . This result answers a question of L. Hörmander. ...

Unbounded Toeplitz operators in the Bargmann-Segal space

J. Janas (1991)

Studia Mathematica

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Weighted-BMO and the Hilbert transform

Hui-Ming Jiang (1991)

Studia Mathematica

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In 1967, E. M. Stein proved that the Hilbert transform is bounded from $L^{\infty}$ to BMO. In 1976, Muckenhoupt and Wheeden gave an analogue of Stein’s result. They gave a necessary and sufficient condition for the boundedness of the Hilbert transform from $L_{w}^{\infty}$ . We improve the results of Muckenhoupt and Wheeden’s and give a necessary and sufficient condition for the boundedness of the Hilbert transform from $B M O_{w}$ to $B M O_{w}$ .

Notes on unbounded Toeplitz operators in Segal-Bargmann spaces

D. Cichoń (1996)

Annales Polonici Mathematici

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Relations between different extensions of Toeplitz operators $T_{φ}$ are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.

$H^{\infty}$ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore, Alberto Venni (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $A$ be the $L^{p}$ realization ( $1 < p < \infty$ ) of a differential operator $P (D_{x}, D_{t})$ on $ℝ^{n} \times ℝ^{+}$ with general boundary conditions $B_{k} (D_{x}, D_{t}) u (x, 0) = 0$ ( $1 \leq k \leq m$ ). Here $P$ is a homogeneous polynomial of order $2 m$ in $n + 1$ complex variables that satisfies a suitable ellipticity condition, and for $1 \leq k \leq m$ $B_{k}$ is a homogeneous polynomial of order $m_{k} < 2 m$ ; it is assumed that the usual complementing condition is satisfied. We prove that $A$ is a sectorial operator with a bounded $H^{\infty}$ functional calculus.