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Some classes of integral equations of convolutions-pair generated by the Kontorovich-Lebedev, Laplace and Fourier transforms

Trinh Tuan
대한수학회 (The Korean Mathematical Society)|2021.07|대한수학회논문집 (Communications of the KMS)|제36권 제3호|pp. 485-494|DOI 10.4134/CKMS.c200183

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키워드

transformConvolutionFourier sineFourier cosineKontorovichh-Lebedev
주제분류수학

초록

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 $(\mathcal{L})$ transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

Abstract

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 $(\mathcal{L})$ transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

참고문헌 (19)

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  17. Trinh TUAN, "A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms", TURKISH JOURNAL OF MATHEMATICS, 44(3), pp.643~655 (2020), The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM)[DOI]
  18. T. Tuan, "On the generalized convolution for the Fourier sine and the Kontorovich-Lebedev transforms", Acta Math. Vietnam, 35(2), pp.303~317 (2010)
  19. S. B. Yakubovich, "Index Transforms" (1996), World Scientific Publishing Co., Inc

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