• Title/Summary/Keyword: Integral Transform

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AN APPROXIMATION OF THE FOURIER SINE TRANSFORM VIA GRÜSS TYPE INEQUALITIES AND APPLICATIONS FOR ELECTRICAL CIRCUITS

  • DRAGOMIR, S.S.;KALAM, A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.1
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    • pp.33-45
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    • 2002
  • An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

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ANALYTIC FOURIER-FEYNMAN TRANSFORMS ON ABSTRACT WIENER SPACE

  • Ahn, Jae Moon;Lee, Kang Lae
    • Korean Journal of Mathematics
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    • v.6 no.1
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    • pp.47-66
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    • 1998
  • In this paper, we introduce an $L_p$ analytic Fourier-Feynman transformation, show the existence of the $L_p$ analytic Fourier-Feynman transforms for a certain class of cylinder functionals on an abstract Wiener space, and investigate its interesting properties. Moreover, we define a convolution product for two functionals on the abstract Wiener space and establish the relationships between the Fourier-Feynman transform for the convolution product of two cylinder functionals and the Fourier-Feynman transform for each functional.

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Convolution product and generalized analytic Fourier-Feynman transforms

  • Chang, Seung-Jun
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.707-723
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    • 1996
  • We first define the concept of the generalized analytic Fourier-Feynman transforms of a class of functionals on function space induced by a generalized Brownian motion process and study of functionals which plays on important role in physical problem of the form $ F(x) = {\int^{T}_{0} f(t, x(t))dt} $ where f is a complex-valued function on $[0, T] \times R$. We next show that the generalized analytic Fourier-Feynman transform of the convolution product is a product of generalized analytic Fourier-Feynman transform of functionals on functin space.

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Incremental Circle Transform Theory and Its Application for Orientation Detection of Two-Dimensional Objects (증분원변환 이론 및 이차원 물체의 자세인식에의 응용)

  • ;;Zeung Nam Bien
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.28B no.7
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    • pp.578-589
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    • 1991
  • In this paper, there is proposed a novel concept of Incremintal Circle Transform which can describe the boundary contour of a two-dimensional object without object without occlusions. And a pattern recognition algorithm to determine the posture of an object is developed with the aid of line integral and similarity transform. Also, It is confirmed via experiments that the algorithm can find the posture of an object in a very fast manner independent of the starting point for boundary coding and the position of the object.

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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Lee, Dong-Myung;Rathie, Arjun K.;Parmar, Rakesh K.;Kim, Yong-Sup
    • Honam Mathematical Journal
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    • v.33 no.2
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    • pp.187-206
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    • 2011
  • The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION

  • Jae Gil Choi;Sang Kil Shim
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.5
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    • pp.1221-1235
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    • 2023
  • In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH VECTOR-VALUED CONDITIONING FUNCTION

  • Ae Young Ko;Jae Gil Choi
    • The Pure and Applied Mathematics
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    • v.30 no.2
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    • pp.155-167
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    • 2023
  • In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functionals which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.