• Title/Summary/Keyword: Dirichlet space

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Multipliers on the dirichlet space $D(Omega)$

  • Nah, Young-Chae
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.633-642
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    • 1995
  • Recently S. Axler proved that every sequence in the unit disk U converging to the boundary contains an interpolating subsequence for the multipliers of the Dirichlet space D(U). In this paper we generalizes Axler's result to the finitely connected planer domains such that the Dirichlet spaces are contained in the Bergman spaces.

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COMMUTANTS OF TOEPLITZ OPERATORS WITH POLYNOMIAL SYMBOLS ON THE DIRICHLET SPACE

  • Chen, Yong;Lee, Young Joo
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.533-542
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    • 2019
  • We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

ZERO SUMS OF DUAL TOEPLITZ PRODUCTS ON THE ORTHOGONAL COMPLEMENT OF THE DIRICHLET SPACE

  • Young Joo, Lee
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.161-170
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    • 2023
  • We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

THE FOCK-DIRICHLET SPACE AND THE FOCK-NEVANLINNA SPACE

  • Cho, Hong Rae;Park, Soohyun
    • East Asian mathematical journal
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    • v.38 no.5
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    • pp.643-647
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    • 2022
  • Let F2 denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F2. We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.