63
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Series expansions of the transform with respect to the Gaussian process

, &
Pages 246-257 | Received 09 Oct 2014, Accepted 19 Nov 2014, Published online: 15 Dec 2014

References

  • Johnson GW, Skoug DL. Scale-invariant measurability in Wiener space. Pacific J Math. 1979;83:157–176. doi: 10.2140/pjm.1979.83.157
  • Lee IY, Chung HS, Chang SJ. Integration formulas involving the transform with respect to the Gaussian process on Wiener space, to submitted for publications.
  • Chung HS, Tuan VK. Fourier-type functionals on Wiener space. Bull Korean Math Soc. 2012;49:609–619. doi: 10.4134/BKMS.2012.49.3.609
  • Chung HS, Choi JG, Chang SJ. Conditional integral transforms with related topics on function space. FILOMAT. 2012;26:1151–1162. doi: 10.2298/FIL1206151C
  • Chung HS, Tuan VK. Generalized integral transforms and convolution products on function space. Integral Transforms Spec Funct. 2011;22:573–586. doi: 10.1080/10652469.2010.535798
  • Lee IY, Chung HS, Chang SJ. Series expansions of the analytic Feynman integral for the Fourier-type functional. J Korean Soc Math Educ Ser B. 2012;19:87–102.
  • Chung HS, Lee IY, Chang SJ. Conditional transform with respect to the Gaussian process involving the conditional convolution product and the first variation. B Korean Math Soc. 2014;51:1561–1577.
  • Chung DM, Park C, Skoug D. Generalized Feynman integrals via conditional Feynman integrals. Michigan Math J. 1993;40:337–391.
  • Kim BS, Skoug D. Integral transforms of functionals in . Rocky Mt J Math. 2003;33:1379–1393. doi: 10.1216/rmjm/1181075469
  • Cameron RH. Some examples of Fourier–Wiener transforms of analytic functionals. Duke Math J. 1945;12:485–488. doi: 10.1215/S0012-7094-45-01243-9
  • Cameron RH, Martin WT. Fourier–Wiener transforms of functionals belonging to over the space C. Duke Math J. 1947;14:99–107. doi: 10.1215/S0012-7094-47-01409-9
  • Chang KS, Kim BS, Song TS, Yoo I. Convolution and analytic Fourier–Feynman transforms over paths in abstract Wiener space. Integral Transforms Spec Funct. 2002;13:345–362. doi: 10.1080/10652460213523
  • Huffman T, Skoug D, Storvick D. Integration formulas involving Fourier–Feynman transforms via a Fubini theorem. J Korean Math Soc. 2001;38:421–435.
  • Park C, Skoug D, Storvick DA. Relationships among the first variation, the convolution product, and the Fourier–Feynman transform. Rocky Mt J Math. 1998;28:277–292. doi: 10.1216/rmjm/1181071725
  • Chang KS, Kim BS, Yoo I. Integral transform and convolution of analytic functionals on abstract Wiener space. Integral Transforms Spec Funct. 2000;21:97–105.
  • Chang SJ, Chung HS, Skoug D. Convolution products, integral transforms and inverse integral transforms of functionals in . Integral Transforms Spec Funct. 2010;21:143–151. doi: 10.1080/10652460903063382
  • Kim BJ, Kim BS, Skoug D. Integral transforms, convolution products, and first variations. Int J Math Sci. 2004;11:579–598. doi: 10.1155/S0161171204305260
  • Chung DM, Park C, Skoug D. Operator valued Feynman integrals via conditional Feynman integrals. Pacific J Math. 1990;1:21–42. doi: 10.2140/pjm.1990.146.21

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.