대한수학회지 (Journal of the Korean Mathematical Society)

  • 제46권2호
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  • Pages.327-345
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  • 2009
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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GENERALIZED FOURIER-WIENER FUNCTION SPACE TRANSFORMS

  • 발행 : 2009.03.31
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초록

In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}[0,\;T]$ to obtain a complete orthonormal set in $L_2(C_{a,b}[0,\;T])$ where $C_{a,b}[0,\;T]$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.

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참고문헌

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피인용 문헌

  1. Relationships Involving Transforms and Convolutions Via the Translation Theorem vol.32, pp.2, 2014, https://doi.org/10.1080/07362994.2013.877350
  2. SERIES EXPANSIONS OF THE ANALYTIC FEYNMAN INTEGRAL FOR THE FOURIER-TYPE FUNCTIONAL vol.19, pp.2, 2012, https://doi.org/10.7468/jksmeb.2012.19.2.87
  3. REFLECTION PRINCIPLES FOR GENERAL WIENER FUNCTION SPACES vol.50, pp.3, 2013, https://doi.org/10.4134/JKMS.2013.50.3.607
  4. Some basic relationships among transforms, convolution products, first variations and inverse transforms vol.11, pp.3, 2013, https://doi.org/10.2478/s11533-012-0148-x
  5. Self-adjoint oscillator operator from a modified factorization vol.375, pp.22, 2011, https://doi.org/10.1016/j.physleta.2011.04.012
  6. Generalized conditional transform with respect to the Gaussian process on function space vol.26, pp.12, 2015, https://doi.org/10.1080/10652469.2015.1070149
  7. generalized analytic Fourier–Feynman transform vol.29, pp.9, 2018, https://doi.org/10.1080/10652469.2018.1497024