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The Wiener Closure Theorems for Abstract Wiener Spaces

J. Kuelbs, V. Mandrekar
1972 Proceedings of the American Mathematical Society  
We introduce y^ and ¥% translates for functions in i(l¡C) andif2(/() where // is a Gaussian measure on a Banach space. With these translates and the Fourier-Wiener transforms defined by Cameron and Martin we obtain Wiener's closure theorem in Sf^(ji) and in ^¡(ji). Using the &,(fi) results we indicate the analogue of the Wiener-Pitt Tauberian theorems for this setup.
doi:10.2307/2038326 fatcat:vzfoxp57ezezthqz673ojits3y