Some basic relationships among transforms, convolution products, first variations and inverse transforms

Seung Chang; Hyun Chung; David Skoug

Open Mathematics (2013)

  • Volume: 11, Issue: 3, page 538-551
  • ISSN: 2391-5455

Abstract

top
In this paper we obtain several basic formulas for generalized integral transforms, convolution products, first variations and inverse integral transforms of functionals defined on function space.

How to cite

top

Seung Chang, Hyun Chung, and David Skoug. "Some basic relationships among transforms, convolution products, first variations and inverse transforms." Open Mathematics 11.3 (2013): 538-551. <http://eudml.org/doc/269220>.

@article{SeungChang2013,
abstract = {In this paper we obtain several basic formulas for generalized integral transforms, convolution products, first variations and inverse integral transforms of functionals defined on function space.},
author = {Seung Chang, Hyun Chung, David Skoug},
journal = {Open Mathematics},
keywords = {Generalized Brownian motion process; Generalized integral transform; Convolution product; First variation; Inverse integral transform; generalized Brownian motion process; generalized integral transform; convolution product; first variation; inverse integral transform},
language = {eng},
number = {3},
pages = {538-551},
title = {Some basic relationships among transforms, convolution products, first variations and inverse transforms},
url = {http://eudml.org/doc/269220},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Seung Chang
AU - Hyun Chung
AU - David Skoug
TI - Some basic relationships among transforms, convolution products, first variations and inverse transforms
JO - Open Mathematics
PY - 2013
VL - 11
IS - 3
SP - 538
EP - 551
AB - In this paper we obtain several basic formulas for generalized integral transforms, convolution products, first variations and inverse integral transforms of functionals defined on function space.
LA - eng
KW - Generalized Brownian motion process; Generalized integral transform; Convolution product; First variation; Inverse integral transform; generalized Brownian motion process; generalized integral transform; convolution product; first variation; inverse integral transform
UR - http://eudml.org/doc/269220
ER -

References

top
  1. [1] Cameron R.H., Martin W.T., Fourier-Wiener transforms of analytic functionals, Duke Math. J., 1945, 12, 489–507 http://dx.doi.org/10.1215/S0012-7094-45-01244-0[Crossref] Zbl0060.27502
  2. [2] Cameron R.H., Martin W.T., Fourier-Wiener transforms of functionals belonging to L 2 over the space C, Duke Math. J., 1947, 14, 99–107 http://dx.doi.org/10.1215/S0012-7094-47-01409-9[Crossref] Zbl0029.40002
  3. [3] Cameron R.H., Storvick D.A., An L 2 analytic Fourier-Feynman transform, Michigan Math. J., 1976, 23(1), 1–30 http://dx.doi.org/10.1307/mmj/1029001617[Crossref] 
  4. [4] Chang K.S., Kim B.S., Yoo I., Integral transform and convolution of analytic functionals on abstract Wiener space, Numer. Funct. Anal. Optim., 2000, 21(1–2), 97–105 [Crossref] Zbl0948.28008
  5. [5] Chang S.J., Choi J.G., Skoug D., Generalized Fourier-Feynman transforms, convolution products and first variations on function space, Rocky Mountain J. Math., 2010, 40(3), 761–788 http://dx.doi.org/10.1216/RMJ-2010-40-3-761[Crossref][WoS] Zbl1202.60133
  6. [6] Chang S.J., Chung D.M., Conditional function space integrals with applications, Rocky Mountain J. Math., 1996, 26(1), 37–62 http://dx.doi.org/10.1216/rmjm/1181072102[Crossref] 
  7. [7] Chang S.J., Chung H.S., Generalized Fourier-Wiener function space transforms, J. Korean Math. Soc., 2009, 46(2), 327–345 http://dx.doi.org/10.4134/JKMS.2009.46.2.327[Crossref] Zbl1178.28024
  8. [8] Chang S.J., Chung H.S., Skoug D., Integral transforms of functionals in L 2(C a;b[0; T]), J. Fourier Anal. Appl., 2009, 15(4), 441–462 http://dx.doi.org/10.1007/s00041-009-9076-y Zbl1185.28023
  9. [9] Chang S.J., Chung H.S., Skoug D., Convolution products, integral transforms and inverse integral transforms of functionals in L 2(C 0[0; T]), Integral Transforms Spec. Funct., 2010, 21(1–2), 143–151 http://dx.doi.org/10.1080/10652460903063382 Zbl1202.28015
  10. [10] Chang S.J., Skoug D., Generalized Fourier-Feynman transforms and a first variation on function space, Integral Transforms Spec. Funct., 2003, 14(5), 375–393 http://dx.doi.org/10.1080/1065246031000074425[Crossref] Zbl1043.28014
  11. [11] Johnson G.W., Skoug D.L., An L p analytic Fourier-Feynman transform, Michigan Math. J., 1979, 26(1), 103–127 http://dx.doi.org/10.1307/mmj/1029002166[Crossref] 
  12. [12] Kim B.J., Kim B.S., Skoug D., Integral transforms, convolution products, and first variations, Int. J. Math. Math. Sci., 2004, 11, 579–598 http://dx.doi.org/10.1155/S0161171204305260[Crossref] Zbl1104.28010
  13. [13] Kim B.S., Skoug D., Integral transforms of functionals in L 2(C 0[0; T]), Rocky Mountain J. Math., 2003, 33(4), 1379–1393 http://dx.doi.org/10.1216/rmjm/1181075469 Zbl1062.28017
  14. [14] Lee Y.J., Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal., 1982, 47(2), 153–164 http://dx.doi.org/10.1016/0022-1236(82)90103-3[Crossref] 
  15. [15] Lee Y.-J., Unitary operators on the space of L 2-functions over abstract Wiener spaces, Soochow J. Math., 1987, 13(2), 165–174 Zbl0661.46042
  16. [16] Nelson E., Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967 Zbl0165.58502
  17. [17] Yeh J., Singularity of Gaussian measures on function spaces induced by Brownian motion processes with nonstationary increments, Illinois J. Math., 1971, 15, 37–46 Zbl0209.19403
  18. [18] Yeh J., Stochastic Processes and the Wiener Integral, Pure Appl. Math. (N.Y.), 13, Marcel Dekker, New York, 1973 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.