본문 바로가기
KERD
논문KCI 등재

Basic formulas for the double integral transform of functionals on abstract Wiener space

정현수
대한수학회 (The Korean Mathematical Society)|2022.09|대한수학회보 (Bulletin of the KMS)|제59권 제5호|pp. 1131-1144|DOI 10.4134/BKMS.b210634

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

Double integral transformdouble convolution productinverse double integral transformabstract Wiener space
주제분류수학

초록

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 \linebreak Wiener space. We then discuss possible relationships involving the double-integral transform.

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 \linebreak Wiener space. We then discuss possible relationships involving the double-integral transform.

참고문헌 (19)

  1. R. H. Cameron, "Fourier-Wiener transforms of analytic functionals", Duke Math. J, 12, pp.489~507 (1945)
  2. R. H. Cameron, "Fourier-Wiener transforms of functionals belonging to L2 over the space C", Duke Math. J, 14, pp.99~107 (1947)
  3. R. H. Cameron, "Analytic continuation for functions of several complex variables", Trans. Amer. Math. Soc, 125, pp.7~12 (1966)[DOI]
  4. ), "Integral Transforms Spec. Funct", 2010, 143~151, https:
  5. K. S. Chang, "Integral transform and convolution of analytic functionals on abstract Wiener space", Numer. Funct. Anal. Optim, 21(1-2), pp.97~105 (2000)[DOI]
  6. D. M. Chung, "Scale-invariant measurability in abstract Wiener spaces", Pacific J. Math, 130(1), pp.27~40 (1987)[DOI]
  7. H. S. Chung, "Generalized integral transforms via the series expressions", Mathematics, 8, pp.539~ (2020)
  8. Hyun Chung, "A matrix transform on function space with related topics", Filomat, 35(13), pp.4459~4468 (2021), National Library of Serbia[DOI]
  9. HYUN SOO CHUNG, "A FUBINI THEOREM FOR INTEGRAL TRANSFORMS AND CONVOLUTION PRODUCTS", International Journal of Mathematics, 24(03), pp.1350024~ (2013), World Scientific Pub Co Pte Lt[DOI]
  10. H. S. Chung, "Double integral transforms and double con"volution products of functionals on abstract Wiener space", Integral Transforms Spec. Funct, 24(11), pp.922~933 (2013)[DOI]
  11. L. Gross, "Abstract Wiener spaces Vol. II: Contributions to Probability Theory", Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, pp.31~42 (1967), Univ. California Press
  12. L. Gross, "Potential theory on Hilbert space", J. Functional Analysis, 1, pp.123~181 (1967)[DOI]
  13. T. Hida, "Transformations for white noise functionals", J. Funct. Anal, 111(2), pp.259~277 (1993)[DOI]
  14. G. W. Johnson, "An Lp analytic Fourier-Feynman transform", Michigan Math. J, 26(1), pp.103~127 (1979)[DOI]
  15. Bong Jin Kim, "Integral transforms, convolution products, and first variations", International Journal of Mathematics and Mathematical Sciences, 2004(11), pp.579~598 (2004), Hindawi Limited[DOI]
  16. ), "Rocky Mountain Journal of Mathematics", 2003, 1379~1393, pp.Rocky Mountain Mathematics Consortium, https:
  17. H. H. Kuo, "Gaussian measures in Banach spaces", Lecture Notes in Mathematics, 463 (1975), Springer-Verlag
  18. Yuh-Jia Lee, "Integral transforms of analytic functions on abstract Wiener spaces", Journal of Functional Analysis, 47(2), pp.153~164 (1982), Elsevier BV[DOI]
  19. Y. J. Lee, "Unitary operators on the space of L2-functions over abstract Wiener spaces", Soochow J. Math, 13(2), pp.165~174 (1987)

관련 논문AI추천

Some relationships between the integral transform and the convolution product on abstract Wiener space이정은, 장승준영남수학회 · East Asian Mathematical Journal2015 · 제31권 제1호Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms박윤정, 임만규, 지운식대한수학회 · 대한수학회보2011 · 제48권 제2호Evaluation formula for Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces장승준, 최재길대한수학회 · 대한수학회보2022 · 제59권 제5호Transforms and convolutions on function space장승준, 최재길대한수학회 · 대한수학회논문집2009 · 제24권 제3호Generalized Fourier–Feynman Transform of Bounded Cylinder Functions on the Function Space C_(a,b)[0, T]최재길경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제2호PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE김병수, 김봉진강원경기수학회 · 한국수학논문집2014 · 제22권 제1호

이 간행물의 다른 논문 (17건)

On the geometry of complex metallic Norden manifoldsRachna Rani, Rakesh Kumar, Adara Monica Blagapp. 1069-1091Evaluation formula for Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces최재길, 장승준pp. 1093-1103Second main theorem with weighted counting functions and uniqueness theoremLiu Yangpp. 1105-1117The Matrix representation of a composition operator on the Hardy space정영복pp. 1119-1129On transcendental meromorphic solutions of certain types of differential equationsAbhijit Banerjee, Sayantan Maity, Tania Biswaspp. 1145-1166
원문 보기