Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Operator-valued Feynman integrals of certain finite-dimensional functionals


Authors: G. W. Johnson and D. L. Skoug
Journal: Proc. Amer. Math. Soc. 24 (1970), 774-780
MSC: Primary 47.70; Secondary 28.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0254675-1
MathSciNet review: 0254675
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {C_0}[a,b]$ denote the space of continuous functions $ x$ on $ [a,b]$ such that $ x(a) = 0$. Let $ F(x) = {f_1}(x({t_1})) \cdots {f_n}(x({t_n}))$ where $ a = {t_0} < {t_1} < \cdots < {t_n} = b$. Recently, Cameron and Storvick defined an operator-valued ``Feynman Integral.'' In their setting, we give a strong existence theorem as well as an explicit formula for the ``Feynman Integral'' of functionals $ F$ as above under weak restrictions on the $ {f_i}$'s. We also give necessary and sufficient conditions for the operator to be invertible and an explicit formula for the inverse.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47.70, 28.00

Retrieve articles in all journals with MSC: 47.70, 28.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0254675-1
Keywords: Feynman integral, Wiener integral, convolution operator, Fourier transform, operator valued Feynman integral
Article copyright: © Copyright 1970 American Mathematical Society