Hyers-Ulam-Rassias stability of Cauchy equation in the space of Schwartz distributions

DOI10.1016/j.jmaa.2004.06.022zbMath1066.39028OpenAlexW2004796662MaRDI QIDQ703656

Jae-Young Chung

Publication date: 11 January 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.06.022

zbMATH Keywords

Cauchy equationtempered distributionsheat kernelsFourier hyperfunctionsGauss transformsrapidly decreasing functions

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Heat equation (35K05) Stability, separation, extension, and related topics for functional equations (39B82) Functional equations for functions with more general domains and/or ranges (39B52)

Related Items (9)

Approximately additive Schwartz distributions ⋮ Stability for quadratic functional equation in the spaces of generalized functions ⋮ Stability of approximately quadratic Schwartz distributions ⋮ Hyers-Ulam-Rassias stability of functional differential systems with point and distributed delays ⋮ Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems ⋮ On Hyers-Ulam-Rassias stability of functional equations ⋮ Stability of multi-additive mappings in non-Archimedean normed spaces ⋮ Uniform exponential stability in the sense of Hyers and Ulam for periodic time varying linear systems ⋮ Generalized stability of multi-additive mappings

Cites Work

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• On the Stability of the Linear Mapping in Banach Spaces
• The Cauchy Functional Equations in Distributions
• On the asymptoticity aspect of Hyers-Ulam stability of mappings
• On the Stability of the Linear Functional Equation
• Distributional methods for functional equations

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