A change of scale formula for a function space integral on Ca,b[0, T]

Il Yoo; Bong Jin Kim; Byoung Soo Kim

doi:10.1090/S0002-9939-2013-11598-4

A change of scale formula for a function space integral on C_a,b[0, T]

Il Yoo
, Bong Jin Kim
, Byoung Soo Kim

School of Natural Sciences

Yonsei University Mirae Campus
Daejin University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B) and in a generalized Fresnel class F_A1,A2 on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on C_a,b[0, T] for functionals in a Banach algebra S(L² _a,b[0, T]). Moreover, we obtain a change of scale formula for a function space integral on C_a,b[0, T] of these functionals.

Original language	English
Pages (from-to)	2729-2739
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-2013-11598-4
State	Published - Aug 2013

Keywords

Change of scale formula
Function space integral
Generalized analytic Feynman integral

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10.1090/S0002-9939-2013-11598-4

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abstract = "Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B) and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on Ca,b[0, T] for functionals in a Banach algebra S(L2 a,b[0, T]). Moreover, we obtain a change of scale formula for a function space integral on Ca,b[0, T] of these functionals.",

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AU - Yoo, Il

AU - Kim, Bong Jin

AU - Kim, Byoung Soo

PY - 2013/8

Y1 - 2013/8

N2 - Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B) and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on Ca,b[0, T] for functionals in a Banach algebra S(L2 a,b[0, T]). Moreover, we obtain a change of scale formula for a function space integral on Ca,b[0, T] of these functionals.

AB - Cameron and Storvick discovered change of scale formulas for Wiener integrals of functionals in a Banach algebra S on classical Wiener space. Yoo and Skoug extended these results for functionals in the Fresnel class F(B) and in a generalized Fresnel class FA1,A2 on abstract Wiener space. We establish a relationship between a function space integral and a generalized analytic Feynman integral on Ca,b[0, T] for functionals in a Banach algebra S(L2 a,b[0, T]). Moreover, we obtain a change of scale formula for a function space integral on Ca,b[0, T] of these functionals.

KW - Change of scale formula

KW - Function space integral

KW - Generalized analytic Feynman integral

UR - https://www.scopus.com/pages/publications/84878166488

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DO - 10.1090/S0002-9939-2013-11598-4

M3 - Article

AN - SCOPUS:84878166488

SN - 0002-9939

VL - 141

SP - 2729

EP - 2739

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

A change of scale formula for a function space integral on C_a,b[0, T]

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Keywords

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