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Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions

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  • Li, Pingrun

Abstract

In this paper we study some classes of generalized singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions. Such equations can be transformed into Riemann boundary value problems with two unknown functions on two parallel straight lines via Fourier transformation. The general solutions and the conditions of solvability are obtained by means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation. This paper will be of great significance for the study of improving and developing complex analysis, integral equation and boundary value problem. Therefore, the classic Riemann boundary value problem is extended further.

Suggested Citation

  • Li, Pingrun, 2019. "Singular integral equations of convolution type with Cauchy kernel in the class of exponentially increasing functions," Applied Mathematics and Computation, Elsevier, vol. 344, pages 116-127.
    • Handle: RePEc:eee:apmaco:v:344-345:y:2019:i::p:116-127
    DOI: 10.1016/j.amc.2018.09.065
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    References listed on IDEAS

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    1. Li, Pingrun, 2017. "Generalized convolution-type singular integral equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 314-323.
    2. Li, Pingrun & Ren, Guangbin, 2016. "Some classes of equations of discrete type with harmonic singular operator and convolution," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 185-194.
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    Cited by:

    1. Zhen-Wei Li & Wen-Biao Gao & Bing-Zhao Li, 2020. "The Solvability of a Class of Convolution Equations Associated with 2D FRFT," Mathematics, MDPI, vol. 8(11), pages 1-12, November.

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