• 대한수학회보
• /
• 제41권1호
• /
• pp.73-93
• /
• 2004

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

• Korean Journal of Mathematics
• /
• 제22권1호
• /
• pp.57-69
• /
• 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.

• Korean Journal of Mathematics
• /
• 제20권1호
• /
• pp.1-18
• /
• 2012

We study various relationships that exist among generalized conditional integral transform, generalized conditional convolution and generalized first variation for a class of functionals defined on K[0, T], the space of complex-valued continuous functions on [0, T] which vanish at zero.

• 호남수학학술지
• /
• 제40권2호
• /
• pp.315-323
• /
• 2018

In this study, firstly we introduce generalized differential and integral operator, also using integral operator two classes are presented. Furthermore, some subordination results involving the Hadamard product (Convolution) for these subclasses of analytic function are proved. A number of consequences of some of these subordination results are also discussed.

• 대한수학회지
• /
• 제41권2호
• /
• pp.265-294
• /
• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.

• Journal of applied mathematics & informatics
• /
• 제42권1호
• /
• pp.65-76
• /
• 2024

In this paper, the I-transform of the Mellin convolution type is presented. Based on the Mellin transform theory, a general integral transform of the Mellin convolution type is introduced. The generating operators for I-transform together with the corresponding operational relations are also presented.

• 대한수학회논문집
• /
• 제36권3호
• /
• pp.485-494
• /
• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• 한국수학사학회지
• /
• 제21권1호
• /
• pp.97-108
• /
• 2008

본 논문에서는 위너공간 위에서 정의되는 해석적 파인만 적분, 해석적 푸리에-파인만 변환과 합성곱을 조사하고 이들에 대한 연구동향에 대하여 알아본다.

• Korean Journal of Mathematics
• /
• 제26권3호
• /
• pp.387-403
• /
• 2018

Shifting, scaling and modulation proprerties for the convolution product of the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal{F}}_{A1,A2}$ are given. These properties help us to obtain convolution product of new functionals from the convolution product of old functionals which we know their convolution product.

• 대한기계학회논문집A
• /
• 제26권5호
• /
• pp.904-913
• /
• 2002

In this paper, the dynamic stress intensity factors of fracture mechanics are numerically computed in time domain using the FEM. For which the finite element formulations are derived applying the Galerkin method to the equations of motion in convolution integral as has been presented in the previous paper. To assure the strain fields of r$^{-1}$ 2/ singularity near the crack tip, the triangular quarter-point singular elements are imbedded in the finite element mesh discretized by the isoparametric quadratic quadrilateral elements. Two-dimensional problems of the elastodynamic fracture mechanics under the impact load are solved and compared with the existing numerical and analytical solutions, being shown that numerical results of good accuracy are obtained by the presented method.