• Title, Summary, Keyword: Integral Transforms

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SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Kachhia, Krunal B.;Prajapati, Jyotindra C.;Purohit, Sunil Dutt
    • Communications of the Korean Mathematical Society
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    • v.31 no.4
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    • pp.779-790
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    • 2016
  • Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS

  • Agarwal, Praveen;Choi, Junesang;Kachhia, Krunal B.;Prajapati, Jyotindra C.;Zhou, Hui
    • Communications of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.591-601
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    • 2016
  • Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.

GENERALIZED ANALYTIC FEYNMAN INTEGRALS INVOLVING GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND GENERALIZED INTEGRAL TRANSFORMS

  • Chang, Seung Jun;Chung, Hyun Soo
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.2
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    • pp.231-246
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    • 2008
  • In this paper, we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish several integration formulas for generalized analytic Feynman integrals generalized analytic Fourier-Feynman transforms and generalized integral transforms of functionals in the class of functionals ${\mathbb{E}}_0$. Finally, we use these integration formulas to obtain several generalized Feynman integrals involving the generalized analytic Fourier-Feynman transform and the generalized integral transform of functionals in ${\mathbb{E}}_0$.

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INTEGRAL TRANSFORMS AND INVERSE INTEGRAL TRANSFORMS WITH RELATED TOPICS ON FUNCTION SPACE I

  • Chang, Seung-Jun;Chung, Hyun-Soo
    • The Pure and Applied Mathematics
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    • v.16 no.4
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    • pp.369-382
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    • 2009
  • In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

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Integral Transforms in Electromagnetic Formulation

  • Eom, Hyo Joon
    • Journal of electromagnetic engineering and science
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    • v.14 no.3
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    • pp.273-277
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    • 2014
  • In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

RELATIONSHIPS BETWEEN INTEGRAL TRANSFORMS AND CONVOLUTIONS ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.51-71
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    • 2013
  • In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

PARTS FORMULAS INVOLVING INTEGRAL TRANSFORMS ON FUNCTION SPACE

  • Kim, Bong-Jin;Kim, Byoung-Soo
    • Communications of the Korean Mathematical Society
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    • v.22 no.4
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    • pp.553-564
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    • 2007
  • In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE

  • Kim, Bong Jin;Kim, Byoung Soo
    • Korean Journal of Mathematics
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    • v.22 no.1
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    • pp.57-69
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    • 2014
  • We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.

CONDITIONAL FOURIER-FEYNMAN TRANSFORMS OF VARIATIONS OVER WIENER PATHS IN ABSTRACT WIENER SPACE

  • Cho, Dong-Hyun
    • Journal of the Korean Mathematical Society
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    • v.43 no.5
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    • pp.967-990
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    • 2006
  • In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.