Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FOURIER-TYPE FUNCTIONALS ON WIENER SPACE

  • Chung, Hyun-Soo (Department of Mathematics Dankook University, Department of Mathematics University of West Georgia) ;
  • Tuan, Vu Kim (Department of Mathematics University of West Georgia)
  • Received : 2011.03.01
  • Published : 2012.05.31
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Abstract

In this paper we define the Fourier-type functionals via the Fourier transform on Wiener space. We investigate some properties of the Fourier-type functionals. Finally, we establish integral transform of the Fourier-type functionals which also can be expressed by other Fourier-type functionals.

Keywords

References

  1. H. H. Bang, Functions with bounded spectrum, Trans. Amer. Math. Soc. 347 (1995), no. 3, 1067-1995. https://doi.org/10.1090/S0002-9947-1995-1283539-1
  2. S. J. Chang, H. S. Chung, and D. Skoug, Convolution products, integral transforms and inverse integral transforms of functionals in $L_{2}(C_{0}[0; T])$, Integral Transforms Spec. Funct. 21 (2010), no. 1-2, 143-151. https://doi.org/10.1080/10652460903063382
  3. H. S. Chung and V. K. Tuan, Generalized integral transforms and convolution products on function space, Integral Transforms Spec. Funct. 22 (2011), no. 8, 573-586. https://doi.org/10.1080/10652469.2010.535798
  4. G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), no. 1, 157-176. https://doi.org/10.2140/pjm.1979.83.157
  5. B. S. Kim and D. Skoug, Integral transforms of functionals in $L_{2}(C_{0}[0; T])$, Rocky Mountain J. Math. 33 (2003), no. 4, 1379-1393. https://doi.org/10.1216/rmjm/1181075469
  6. Y. J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), no. 2, 153-164. https://doi.org/10.1016/0022-1236(82)90103-3
  7. R. E. A. C. Paley, N. Wiener and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), no. 1, 647-688. https://doi.org/10.1007/BF01474606
  8. C. Park, A generalized Paley-Wiener-Zygmund integrals and applications, Proc. Amer. Math. Soc. 23 (1969), 388-400. https://doi.org/10.1090/S0002-9939-1969-0245752-1
  9. C. Park and D. Skoug, A note on Paley-Wiener-Zygmund stochastic integrals, Proc. Amer. Math. Soc. 103 (1988), no. 2, 591-601. https://doi.org/10.1090/S0002-9939-1988-0943089-8
  10. E. M. Stein and G.Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
  11. V. K. Tuan, Paley-Wiener type theorems, Fract. Calc. Appl. Anal. 2 (1999), no. 2, 135-143.

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