Functional Analysis and the Feynman Operator Calculus

“The book is a self-contained treatise on the mathematical foundation of Feynman operational calculus and Feynman path integrals. … It contains a large amount of original material which cannot be found elsewhere in book form; in fact, most of the original results are due to the authors themselves. … The book will be of interest to both graduate students and researchers in pure or applied mathematics.” (Sonia Mazzucchi, Mathematical Reviews, November, 2016)“This book carries Fujiwara's insight to provide the mathematical frameworks for Feynman's operator calculus and for the Feynman path integral. … The book is intended for advanced graduate students and researchers and can be used as a text for advanced courses in functional analysis, operator theory, mathematical physics, or related subjects.” (Miyeon Kwon, zbMATH 1345.81001, 2016)>

• Preliminary Background.- Integration on Infinite-dimensional Spaces.- HK-Integral and HK-Spaces.- Analysis on Hilbert Space.- Operators on Banach Space.- Spaces of von Neumann Type.- The Feynman Operator Calculus.- Applications of the Feynman Calculus.