Abstract
Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra Ŝ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or continuous. Also we study the relationships involving this transform and the first variation.
| Original language | English |
|---|---|
| Pages (from-to) | 1819-1838 |
| Number of pages | 20 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 360 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2008 |
Keywords
- Convolution
- Parseval's relation
- Sequential Feynman integral
- Sequential Fourier-Feynman transform
- Translation theorem