Applications of the Fourier-Wiener Transform to Differential Equations on Infinite Dimensional Spaces. I

DOI10.2307/1999982zbMath0453.28010OpenAlexW4234927515MaRDI QIDQ3900297

Yuh-Jia Lee

Publication date: 1980

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/1999982

zbMATH Keywords

Wiener measureabstract Wiener spaceexponential type analytic functionsequicontinuous semigroup of class (Co)exponential type analytic functionFourier-Wiener c-transform

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Series solutions to PDEs (35C10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Initial value problems for higher-order parabolic equations (35K30) Initial value problems for higher-order hyperbolic equations (35L30) Higher-order elliptic equations (35J30)

Related Items

Sharp inequalities and regularity of heat semigroup on infinite dimensional spaces, Convolution and the Fourier-Wiener transform on abstract Wiener space, Applications of the Fourier-Wiener transform to differential equations on infinite dimensional spaces. II, Unitary representations of a loop \(ax+b\) group, Wiener measure and \(\Gamma \)-function, Unnamed Item, Integral transforms of analytic functions on abstract Wiener spaces, Unnamed Item, A survey of results involving transforms and convolutions in function space, Generalized functions on infinite dimensional spaces and its applications to white noise calculus, Solutions of infinite dimensional partial differential equations