East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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THE FOCK-DIRICHLET SPACE AND THE FOCK-NEVANLINNA SPACE

  • Cho, Hong Rae (Department of Mathematics, Pusan National University) ;
  • Park, Soohyun (Department of Mathematics, Pusan National University)
  • Received : 2022.06.07
  • Accepted : 2022.09.30
  • Published : 2022.09.30
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Abstract

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 $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

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Acknowledgement

This work was financially supported by a 2-Year Research Grant of Pusan National University.

References

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