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http://dx.doi.org/10.5831/HMJ.2022.44.3.447

THE POLYANALYTIC SUB-FOCK REPRODUCING KERNELS WITH CERTAIN POSITIVE INTEGER POWERS

Kim, Hyeseon (Department of Mathematics Education, Wonkwang University)

Publication Information

Honam Mathematical Journal / v.44, no.3, 2022 , pp. 447-460 More about this Journal

Abstract

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space A^α,m_q (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 K^ℂ_α,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 K^ℂ_α,q,m(z, w) is zero-free.

Keywords

Mittag-Leffler function; orthogonal polynomials; polyanalytic functions; reproducing kernel; weighted Laguerre polynomial;

Citations & Related Records

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