Heat and Laplace type equations with complex spatial variables in weighted Fock spaces
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Date
2020-10-30
Authors
Gal, Ciprian G.
Gal, Sorin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In a recent book co-authored by the authors of this article, we studied by semigroup theory methods several classical evolution equations, including the heat and Laplace equations, with real time variable and complex spatial variable, under the hypothesis that the boundary function belongs to the space of analytic functions in the open unit disk and continuous in the closed unit disk, endowed with the uniform norm. Also, in a subsequent paper, the authors have extended the results for the heat and Laplace equations in weighted Bergman spaces on the unit disk. The purpose of this article is to show that the semigroup theory methods work for these two evolution equations of complex spatial variables, under the hypothesis that the boundary function belongs to the weighted Fock space on ℂ, Fpα(ℂ), with 1 ≤ p < +∞, endowed with the Lp-norm. Also, the case of several complex variables is considered. The proofs use the Jensen's inequality, Fubini's theorem for integrals and the Lp-integral modulus of continuity.
Description
Keywords
Complex spatial variable, Semigroups of linear operators, Heat equation, Laplace equation, Weighted Fock space
Citation
Gal, C. G., & Gal, S. G. (2020). Heat and Laplace type equations with complex spatial variables in weighted Fock spaces. <i>Electronic Journal of Differential Equations, 2020</i>(109), pp. 1-10.
Rights
Attribution 4.0 International