In this paper, we investigate two approaches to the use of unbounded operators in Feynman’s operational calculus. The first involves using a functional calculus for unbounded operators introduced by A. E. Taylor in the paper . The second approach uses analytic families of closed unbounded operators as discussed in . For each approach, we discuss the essential properties of the operational calculus as well as continuity (or stability) properties. Finally, for the approach using the Taylor calculus, we discussion a connection between Feynman’s operational calculus in this setting with the Modified Feynman Integral of M. L. Lapidus ([14, 20]).
|Original language||English (US)|
|Number of pages||68|
|Journal||New York Journal of Mathematics|
|State||Published - Jan 1 2020|
All Science Journal Classification (ASJC) codes