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

A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation 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 p into L p^\prime (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 Schrödinger 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

, Volume 48 (1) – Jun 6, 2003
26 pages

/lp/springer_journal/a-generalized-analytic-operator-valued-function-space-integral-and-a-JQ7ENigZkU
Publisher
Springer-Verlag
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-003-0769-3
Publisher site
See Article on Publisher Site

### Abstract

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 p into L p^\prime (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 Schrödinger 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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 6, 2003

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