A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation

Journal Article · Fri Jun 06 00:00:00 EDT 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-003-0769-3· OSTI ID:21064233

Chang, K S; kr, mathkbs@yonsei ac

We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L{sub p} into L{sub p-ci{sub r}}{sub cumflexprime}(1<p {<=} 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schroedinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results.

• OSTI ID: 21064233
• Journal Information: Applied Mathematics and Optimization, Vol. 48, Issue 1; Other Information: DOI: 10.1007/s00245-003-0769-3; Copyright (c) 2003 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 2003 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FUNCTIONALS
INTEGRAL EQUATIONS
INTEGRALS
MARKOV PROCESS
MATHEMATICAL SPACE
SCHROEDINGER EQUATION