Classes of transforms associated with bounded linear operators on abstract Wiener spaces

Abstract

In this article, we study an algebraic structure of the analytic Fourier--Feynman transform (FFT) associated with bounded linear operators on abstract Wiener space (AWS). It turned out in this paper that a class of the analytic FFTs forms a monoid and that a quotient monoid is isomorphic to the monoid of the FFTs. Additionally, we provide a transformation group freely generated by FFTs. Any transforms in the free group are linear operator isomorphisms.