Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions
Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/9235960 |
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| author | Dong Hyun Cho |
| author_facet | Dong Hyun Cho |
| author_sort | Dong Hyun Cho |
| collection | DOAJ |
| description | Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself. |
| format | Article |
| id | doaj-art-79ada9a0280e43a9bc34e77b3bfedf87 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-79ada9a0280e43a9bc34e77b3bfedf872025-02-03T06:11:35ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/92359609235960Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal DistributionsDong Hyun Cho0Department of Mathematics, Kyonggi University, Suwon 16227, Republic of KoreaUsing simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself.http://dx.doi.org/10.1155/2016/9235960 |
| spellingShingle | Dong Hyun Cho Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions Journal of Function Spaces |
| title | Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions |
| title_full | Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions |
| title_fullStr | Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions |
| title_full_unstemmed | Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions |
| title_short | Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions |
| title_sort | integral transforms on a function space with change of scales using multivariate normal distributions |
| url | http://dx.doi.org/10.1155/2016/9235960 |
| work_keys_str_mv | AT donghyuncho integraltransformsonafunctionspacewithchangeofscalesusingmultivariatenormaldistributions |