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A generalized integral transform with the kernel on function space with related topics

정현수
대한수학회 (The Korean Mathematical Society)|2024.09|대한수학회보 (Bulletin of the KMS)|제61권 제5호|pp. 1253-1267|DOI 10.4134/BKMS.b230499

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키워드

Wiener spaceFubini theoremIntegral transformcomposition formulaCameron-Storvick type theorem
주제분류수학

초록

In this paper, we define a generalized integral transform $\mathcal{T}_\alpha$ on function space. We then establish some fundamental formulas for the integral transform $\mathcal{T}_\alpha$ involving the convolution product and the first variation. Furthermore, we establish some relationships among the integral transform, the convolution product and the first variation. Finally, we state an application with some examples.

Abstract

In this paper, we define a generalized integral transform $\mathcal{T}_\alpha$ on function space. We then establish some fundamental formulas for the integral transform $\mathcal{T}_\alpha$ involving the convolution product and the first variation. Furthermore, we establish some relationships among the integral transform, the convolution product and the first variation. Finally, we state an application with some examples.

참고문헌 (15)

  1. R. H. Cameron, "Some examples of Fourier-Wiener transforms of analytic functionals", Duke Math. J, 12(3), pp.485~488 (1945)
  2. S. J. Chang, "A recurrence formula with respect to the Cameron-Storvick type theorem of the T-transform", Integral Transforms Spec. Funct, 31(4), pp.323~338 (2020)[DOI]
  3. ), "Integral Transforms Spec. Funct", 2010, 143~151, 10.1080[DOI]
  4. 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]
  5. H. S. Chung, "A matrix transform on function space with related topics", Filomat, 35(13), pp.4459~4468 (2021)
  6. H. S. Chung, "Basic formulas for the double integral transform of functionals on abstract Wiener space", Bull. Korean Math. Soc, 59(5), pp.1131~1144 (2022)[DOI]
  7. H. S. Chung, "An integral transform via the bounded linear operators on abstract Wiener space", Filomat, 37(17), pp.5541~5552 (2023)
  8. D. M. Chung, "Transforms on white noise functionals with their applications to Cauchy problems", Nagoya Math. J, 147, pp.1~23 (1997)[DOI]
  9. H. S. Chung, "A Fubini theorem for integral transforms and convolution products", Internat. J. Math, 24(3), pp.1350024~ (2013)[DOI]
  10. H. S. Chung, "Generalized integral transforms and convolution products on function space", Integral Transforms Spec. Funct, 22(8), pp.573~586 (2011)[DOI]
  11. M. K. Im, "Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms", Bull. Korean Math. Soc, 48(2), pp.291~302 (2011)[DOI]
  12. B. J. Kim, "Integral transforms, convolution products, and first variations", Int. J. Math. Math. Sci, 2004(11), pp.579~598 (2004)[DOI]
  13. ), "Rocky Mountain J. Math", 2003, 1379~1393, 10.1216[DOI]
  14. Y. -J. Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Functional Analysis, 47(2), pp.153~164 (1982)[DOI]
  15. Y. -J. Lee, "Unitary operators on the space of L2-functions over abstract Wiener spaces", Soochow J. Math, 13(2), pp.165~174 (1987)

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