A REPRESENTATION FOR THE INVERSE GENERALISED FOURIER–FEYNMAN TRANSFORM VIA CONVOLUTION PRODUCT ON FUNCTION SPACE
2017 ◽
Vol 95
(3)
◽
pp. 424-435
Keyword(s):
We study a representation for the inverse transform of the generalised Fourier–Feynman transform on the function space $C_{a,b}[0,T]$ which is induced by a generalised Brownian motion process. To do this, we define a transform via the concept of the convolution product of functionals on $C_{a,b}[0,T]$. We establish that the composition of these transforms acts like an inverse generalised Fourier–Feynman transform and that the transforms are vector space automorphisms of a vector space ${\mathcal{E}}(C_{a,b}[0,T])$. The vector space ${\mathcal{E}}(C_{a,b}[0,T])$ consists of exponential-type functionals on $C_{a,b}[0,T]$.
2002 ◽
Vol 29
(10)
◽
pp. 591-608
◽
2000 ◽
Vol 23
(11)
◽
pp. 759-776
◽