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dc.contributor.authorGal, Ciprian G. ( Orcid Icon 0000-0002-6408-2565 )
dc.contributor.authorGal, Sorin ( )
dc.date.accessioned2021-10-08T18:48:10Z
dc.date.available2021-10-08T18:48:10Z
dc.date.issued2020-10-30
dc.identifier.citationGal, C. G., & Gal, S. G. (2020). Heat and Laplace type equations with complex spatial variables in weighted Fock spaces. Electronic Journal of Differential Equations, 2020(109), pp. 1-10.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14620
dc.description.abstractIn 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.en_US
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectComplex spatial variableen_US
dc.subjectSemigroups of linear operatorsen_US
dc.subjectHeat equationen_US
dc.subjectLaplace equationen_US
dc.subjectWeighted Fock spaceen_US
dc.titleHeat and Laplace type equations with complex spatial variables in weighted Fock spacesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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