Heat and Laplace type equations with complex spatial variables in weighted Bergman spaces

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dc.contributor.authorGal, Ciprian G.
dc.contributor.authorGal, Sorin
dc.date.accessioned2022-07-27T21:27:45Z
dc.date.available2022-07-27T21:27:45Z
dc.date.issued2017-09-29
dc.description.abstractIn a recent book, the authors of this paper have studied the classical heat and Laplace equations with real time variable and complex spatial variable by the semigroup theory methods, 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. The purpose of the present note is to show that the semigroup theory methods works for these evolution equations of complex spatial variables, under the hypothesis that the boundary function belongs to the much larger weighted Bergman space Bpα with 1 ≤ p < +∞, endowed with a Lp-norm. Also, the case of several complex variables is considered. The proofs require some new changes appealing to Jensen's inequality, Fubini's theorem for integrals and the Lp-integral modulus of continuity. The results obtained can be considered as complex analogues of those for the classical heat and Laplace equations in Lp(ℝ) spaces.
dc.description.departmentMathematics
dc.formatText
dc.format.extent8 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationGal, C. G., & Gal, S. G. (2017). Heat and Laplace type equations with complex spatial variables in weighted Bergman spaces. <i>Electronic Journal of Differential Equations, 2017</i>(236), pp. 1-8.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16005
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectComplex spatial variable
dc.subjectSemigroups of linear operators
dc.subjectHeat equation
dc.subjectLaplace equation
dc.subjectWeighted Bergman space
dc.titleHeat and Laplace type equations with complex spatial variables in weighted Bergman spaces
dc.typeArticle

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