A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II
We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,...,(hn,x)∼), x∈B where μˆ:ℝn→ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ(ℝn), the Borel σ-algebra of ℝn with ‖μ‖<∞, the analytic Feynman integral of F exists, although the analytic Feynman i...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004537 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564358728646656 |
|---|---|
| author | Young Sik Kim |
| author_facet | Young Sik Kim |
| author_sort | Young Sik Kim |
| collection | DOAJ |
| description | We show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,...,(hn,x)∼), x∈B where μˆ:ℝn→ℂ is
the Fourier-transform of the complex-valued Borel measure μ on ℬ(ℝn), the Borel σ-algebra of
ℝn with ‖μ‖<∞, the analytic Feynman
integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not
always exist for bounded cylinder functions F(x)=f((h1,x)∼,...,(hn,x)∼), x∈B. We prove a change of scale formula for Wiener integrals of F on
the abstract Wiener space. |
| format | Article |
| id | doaj-art-cac74e4698c9421ea5c33cdb4b0f85ba |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cac74e4698c9421ea5c33cdb4b0f85ba2025-02-03T01:11:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125423123710.1155/S0161171201004537A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space IIYoung Sik Kim0BK-21 Mathematical Science Division, Department of Mathematics, Seoul National University, Seoul 151-742, South KoreaWe show that for certain bounded cylinder functions of the form F(x)=μˆ((h1,x)∼,...,(hn,x)∼), x∈B where μˆ:ℝn→ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ(ℝn), the Borel σ-algebra of ℝn with ‖μ‖<∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not always exist for bounded cylinder functions F(x)=f((h1,x)∼,...,(hn,x)∼), x∈B. We prove a change of scale formula for Wiener integrals of F on the abstract Wiener space.http://dx.doi.org/10.1155/S0161171201004537 |
| spellingShingle | Young Sik Kim A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II International Journal of Mathematics and Mathematical Sciences |
| title | A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II |
| title_full | A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II |
| title_fullStr | A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II |
| title_full_unstemmed | A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II |
| title_short | A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II |
| title_sort | change of scale formula for wiener integrals of cylinder functions on the abstract wiener space ii |
| url | http://dx.doi.org/10.1155/S0161171201004537 |
| work_keys_str_mv | AT youngsikkim achangeofscaleformulaforwienerintegralsofcylinderfunctionsontheabstractwienerspaceii AT youngsikkim changeofscaleformulaforwienerintegralsofcylinderfunctionsontheabstractwienerspaceii |