Integral transforms on a function space with change of scales using multivariate normal distributions
type: Item
instance of: scholarly article
title: Integral transforms on a function space with change of scales using multivariate normal distributions
zbMATH Open document ID: 1354.46046
DOI: 10.1155/2016/9235960
author: Dong Hyun Cho
published in: Journal of Function Spaces
publication date: 2016-06-30T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 81S40
zbMATH DE Number: 6599828
zbMATH Keywords: conditional Wiener integrals
zbMATH Keywords: generalized cylinder function
zbMATH Keywords: Feynman integration
Wikidata QID: Q59126589
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9235960
OpenAlex ID: W2417996216
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description: scientific article; zbMATH DE number 6599828