• 대한수학회논문집
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• 제36권3호
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• pp.485-494
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• 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.

• 대한전자공학회논문지
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• 제26권7호
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• pp.1-7
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• 1989

가장자리로 부터 역비례로 저항률이 변하는 반평면에 H분극 평면파가 입사되는 경우, 산란파를 Kontorovich-Lebedev 변환을 이용해서 정확한 적분식으로 얻었으며, 이로부터 모든 각도에서 쓸 수 있는 균일 근사식 및 계산된 산란파를 광선적(光線的)으로 해석할 수 있도록 해주는 비균일 근사식도 구했다. 저항율의 상수 여러 값에 대하여 가장자리 회절 패턴을 보였다. 결과들은 물리적으로 타당함을 알 수 있었다.

• Journal of electromagnetic engineering and science
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• 제14권3호
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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.

• 대한수학회지
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• 제40권6호
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• pp.999-1014
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• 2003

For a fixed function h we deal with a class of convolution transforms $f\;{\rightarrow}\;f\;*\;h$, where $(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}$ as integral operators $L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.