Some basic relationships among transforms, convolution products, first variations and inverse transforms
Seung Chang ; Hyun Chung ; David Skoug
Open Mathematics, Tome 11 (2013), p. 538-551 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:269220
@article{bwmeta1.element.doi-10_2478_s11533-012-0148-x,
     author = {Seung Chang and Hyun Chung and David Skoug},
     title = {Some basic relationships among transforms, convolution products, first variations and inverse transforms},
     journal = {Open Mathematics},
     volume = {11},
     year = {2013},
     pages = {538-551},
     zbl = {1260.28013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0148-x}
}
Seung Chang; Hyun Chung; David Skoug. Some basic relationships among transforms, convolution products, first variations and inverse transforms. Open Mathematics, Tome 11 (2013) pp. 538-551. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0148-x/

[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] | Zbl 0060.27502

[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] | Zbl 0029.40002

[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] 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] | Zbl 0948.28008

[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] | Zbl 1202.60133

[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] 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] | Zbl 1178.28024

[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 | Zbl 1185.28023

[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 | Zbl 1202.28015

[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] | Zbl 1043.28014

[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] 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] | Zbl 1104.28010

[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 | Zbl 1062.28017

[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] Lee Y.-J., Unitary operators on the space of L 2-functions over abstract Wiener spaces, Soochow J. Math., 1987, 13(2), 165–174 | Zbl 0661.46042

[16] Nelson E., Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967 | Zbl 0165.58502

[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 | Zbl 0209.19403

[18] Yeh J., Stochastic Processes and the Wiener Integral, Pure Appl. Math. (N.Y.), 13, Marcel Dekker, New York, 1973