Density of Complex and Quaternionic Polyanalytic Polynomials in Polyanalytic Fock Spaces
Complex Analysis and Operator Theory（2024）
摘要
In this paper we consider the polyanalytic Fock spaces both in the complex and in the quaternionic case. In this latter case, the polyanalytic functions are considered in the slice regular case, and we shall treat Fock spaces of the first and of the second kind. In all these spaces we prove quantitative results in the approximation by polyanalytic polynomials. The quantitative approximation results are given in terms of higher order L^p -moduli of smoothness.
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关键词
Polyanalytic complex Fock space,Polyanalytic complex functions,Polyanalytic complex polynomials,Polyanalytic quaternionic Fock space of the first kind,Polyanalytic quaternionic Fock space of second kind,Slice quaternionic polyanalytic functions,Slice quaternionic polyanalytic polynomials,Convolution with trigonometric kernels,Quantitative estimates,L -moduli of smoothness,Slice regular functions,Best approximation,Primary 30E10,30G35,Secondary 41A25
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