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2013 | 11 | 3 | 538-551
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
3
Strony
538-551
Opis fizyczny
Daty
wydano
2013-03-01
online
2012-12-22
Twórcy
autor
autor
autor
  • Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0130, USA, dskoug@math.unl.edu
Bibliografia
  • [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]
  • [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]
  • [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]
  • [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]
  • [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]
  • [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
  • [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
  • [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]
  • [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]
  • [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
  • [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
  • [16] Nelson E., Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967
  • [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
  • [18] Yeh J., Stochastic Processes and the Wiener Integral, Pure Appl. Math. (N.Y.), 13, Marcel Dekker, New York, 1973
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0148-x
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