호남수학학술지 (Honam Mathematical Journal)

  • 제44권3호
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  • Pages.447-460
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  • 2022
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE POLYANALYTIC SUB-FOCK REPRODUCING KERNELS WITH CERTAIN POSITIVE INTEGER POWERS

  • Kim, Hyeseon (Department of Mathematics Education, Wonkwang University)
  • 투고 : 2022.07.18
  • 심사 : 2022.08.03
  • 발행 : 2022.09.01
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초록

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space Aα,mq (ℂ) of q-analytic functions with the weight ϕ(z) = -α log |z|2+|z|2m for any positive integer m. We obtain the corresponding reproducing kernel Kℂα,q,m(z, w) using the weighted Laguerre polynomials and the Mittag-Leffler functions. Finally, we investigate the necessary and sufficient condition on (α, q, m) such that Kℂα,q,m(z, w) is zero-free.

키워드

과제정보

The author thanks to the anonymous referees for their valuable comments. The author also thanks to Jong-Do Park for many fruitful discussions. This work was supported by the National Research Foundation of Korea under grant number NRF-2018R1D1A1B07044363.

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