Browse > Article
http://dx.doi.org/10.4134/BKMS.b210634

BASIC FORMULAS FOR THE DOUBLE INTEGRAL TRANSFORM OF FUNCTIONALS ON ABSTRACT WIENER SPACE  

Chung, Hyun Soo (Department of Mathematics Dankook University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.5, 2022 , pp. 1131-1144 More about this Journal
Abstract
In this paper, we establish several basic formulas among the double-integral transforms, the double-convolution products, and the inverse double-integral transforms of cylinder functionals on abstract Wiener space. We then discuss possible relationships involving the double-integral transform.
Keywords
Double integral transform; double convolution product; inverse double integral transform; abstract Wiener space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. J. Chang, H. S. Chung, and D. Skoug, Convolution products, integral transforms and inverse integral transforms of functionals in L2(C0[0, T]), Integral Transforms Spec. Funct. 21 (2010), no. 1-2, 143-151. https://doi.org/10.1080/10652460903063382   DOI
2 K. S. Chang, B. S. Kim, and I. Yoo, Integral transform and convolution of analytic functionals on abstract Wiener space, Numer. Funct. Anal. Optim. 21 (2000), no. 1-2, 97-105. https://doi.org/10.1080/01630560008816942   DOI
3 D. M. Chung, Scale-invariant measurability in abstract Wiener spaces, Pacific J. Math. 130 (1987), no. 1, 27-40. http://projecteuclid.org/euclid.pjm/1102690291   DOI
4 H. S. Chung, Generalized integral transforms via the series expressions, Mathematics 8 (2020), 539.
5 H. S. Chung, A matrix transform on function space with related topics, Filomat 35 (2021), no 13, 4459-4468. https://doi.org/10.2298/FIL2113459C   DOI
6 H. S. Chung, D. Skoug, and S. J. Chang, Double integral transforms and double convolution products of functionals on abstract Wiener space, Integral Transforms Spec. Funct. 24 (2013), no. 11, 922-933. https://doi.org/10.1080/10652469.2013.783577   DOI
7 H. S. Chung, D. Skoug, and S. J. Chang, A Fubini theorem for integral transforms and convolution products, Internat. J. Math. 24 (2013), no. 3, 1350024, 13 pp. https://doi.org/10.1142/S0129167X13500249   DOI
8 L. Gross, Potential theory on Hilbert space, J. Functional Analysis 1 (1967), 123-181. https://doi.org/10.1016/0022-1236(67)90030-4   DOI
9 B. S. Kim and D. Skoug, Integral transforms of functionals in L2(C0[0, T]), Rocky Mountain J. Math. 33 (2003), no. 4, 1379-1393. https://doi.org/10.1216/rmjm/1181075469   DOI
10 R. H. Cameron and D. A. Storvick, Analytic continuation for functions of several complex variables, Trans. Amer. Math. Soc. 125 (1966), 7-12. https://doi.org/10.2307/1994584   DOI
11 T. Hida, H.-H. Kuo, and N. Obata, Transformations for white noise functionals, J. Funct. Anal. 111 (1993), no. 2, 259-277. https://doi.org/10.1006/jfan.1993.1012   DOI
12 G. W. Johnson and D. L. Skoug, An Lp analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), no. 1, 103-127. http://projecteuclid.org/euclid.mmj/1029002166   DOI
13 B. J. Kim, B. S. Kim, and D. Skoug, Integral transforms, convolution products, and first variations, Int. J. Math. Math. Sci. 2004 (2004), no. 9-12, 579-598. https://doi.org/10.1155/S0161171204305260   DOI
14 Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Functional Analysis 47 (1982), no. 2, 153-164. https://doi.org/10.1016/0022-1236(82)90103-3   DOI
15 Y. J. Lee, Unitary operators on the space of L2-functions over abstract Wiener spaces, Soochow J. Math. 13 (1987), no. 2, 165-174.
16 R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of functionals belonging to L2 over the space C, Duke Math. J. 14 (1947), 99-107. http://projecteuclid.org/euclid.dmj/1077473992   DOI
17 R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of analytic functionals, Duke Math. J. 12 (1945), 489-507. http://projecteuclid.org/euclid.dmj/1077473257   DOI
18 L. Gross, Abstract Wiener spaces, in Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 1, 31-42, Univ. California Press, Berkeley, CA, 1967.
19 H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, Vol. 463, Springer-Verlag, Berlin, 1975.