Positivity and positive definiteness in generalized function algebras

DOI10.1016/j.jmaa.2006.06.034zbMath1116.46031OpenAlexW2102832334MaRDI QIDQ864647

Stevan Pilipović, Michael Oberguggenberger, Dimitris Scarpalézos

Publication date: 12 February 2007

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.2006.06.034

zbMATH Keywords

positive and positivity definite generalized functionsspecial Colombeau algebra

Mathematics Subject Classification ID

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (9)

Generalized stochastic processes in algebras of generalized functions: independence, stationarity and SPDEs ⋮ Probabilistic properties of generalized stochastic processes in algebras of generalized functions ⋮ New topologies on Colombeau generalized numbers and the Fermat-Reyes theorem ⋮ Foundations of the calculus of variations in generalized function algebras ⋮ Symplectic Modules Over Colombeau-Generalized Numbers ⋮ Harmonic generalized functions in generalized function algebras ⋮ Real analytic generalized functions ⋮ Generalized stochastic processes in algebras of generalized functions ⋮ Algebras of generalized functions with smooth parameter dependence

Cites Work

• Generalized solutions to nonlinear first-order systems
• Borel's theorem for generalized functions
• Generalized solutions of nonlinear differential equation and the maslov algebras of distributions
• A contribution to the theory of generalized functions
• A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise
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