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Some relationships between the integral transform and the convolution product on abstract Wiener space

장승준|이정은
영남수학회 (Youngnam Mathematical Society)|2015.01|East Asian Mathematical Journal|제31권 제1호|pp. 135-144|DOI http://dx.doi.org/10.7858/eamj.2015.014

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참고문헌

키워드

Abstract Wiener spaceintegral transformconvolution productFubini theorem
주제분류수학

초록

In this paper we establish several formulas for multiple integral transform of functionals definedon abstract Wiener space. We then use the these results to establish several basic formulasinvolving multiple convolution products.

Abstract

In this paper we establish several formulas for multiple integral transform of functionals definedon abstract Wiener space. We then use the these results to establish several basic formulasinvolving multiple convolution products.

참고문헌 (13)

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  7. 임만규, "Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms", 대한수학회보, 48(2), pp.291~302 (2011), 대한수학회
  8. G.W. Johnson, "Scale-invariant measurability in Wiener space", Pacific J. Math, 83, pp.157~176 (1979)
  9. H.-H. Kuo, "Gaussian Measures in Banach Spaces", Lecture Note in Mathematics, 463, pp.579~598 (1980), Springer
  10. B.J. Kim, "Integral transforms, convolution products and first variations", Int. J. Math. Math. Soc, 11, pp.579~598 (2004)
  11. ), "Rocky Moun-tain J. Math", 2003, 1379~1393
  12. Y.J. Lee, "Applications of the Fourier-Wiener transform to di erential equations on infinite dimensional spaces I", Trans. Amer. Math. Soc, 262, pp.259~283 (1980)
  13. Y.J. Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Funct. Anal, 47, pp.153~164 (1982)

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