Duality of fundamental solutions of parabolic equations in infinite dimensions

DOI10.1016/0022-247X(81)90027-5zbMath0455.35002OpenAlexW2005586782MaRDI QIDQ1150088

M. Ann. Piech

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0022-247x(81)90027-5

zbMATH Keywords

uniquenessfundamental solutionboundssmoothnessadjoint equationabstract Wiener spaceLebesgue measuresemigroup propertyduality relationshiphomogeneous second order parabolic equationparabolic equations in infinite dimensionsRadon- Nikodym derivative

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) General theory of partial differential operators (47F05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Parabolic equations and parabolic systems (35K99)

Cites Work

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• Opérateurs pseudo-différentiels en dimension infinie. Étude de l'hypoellipticite et de la resolubilite dans des classes de fonctions hölderiennes et de distributions pour des opérateurs pseudo- différentiels elliptiques
• Potential theory on Hilbert space
• A fundamental solution of the parabolic equation on Hilbert space
• Some regularity properties of diffusion processes on abstract Wiener space
• Differentiability of Measures Associated with Parabolic Equations on Infinite Dimensional Spaces
• Dirichlet forms and diffusion processes on rigged Hilbert spaces
• A Fundamental Solution of the Parabolic Equation on Hilbert Space. II: The Semigroup Property
• Harmonic analysis on Hilbert space
• Linear second-order partial differential equations of the parabolic type

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