Generalized boundary value problems for analytic functions with convolutions and its applications. (28th February 2019)

• Record Type: Journal Article
• Authors: Li, Pingrun
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 8(2019)
• Page Start: 2631
• Page End: 2645
• Publication Date: 2019-02-28
• Subjects: boundary value problems for analytic functions -- convolution kernel -- integral operator -- locality theory -- singular integral equations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5538
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we first establish a locality theory for the Noethericity of generalized boundary value problems on the spaces L p ( R ) ( 1 ≤ p < ∞ ) . By means of this theory, of the classical boundary value theory, and of the theory of Fourier analysis, we discuss the necessary and sufficient conditions of the solvability and obtain the general solutions and the Noether conditions for one class of generalized boundary value problems. All cases as regards the index of the coefficients in the equations are considered in detail. Moreover, we apply our theoretical results to the solvability of singular integral equations with variable coefficients. Thus, this paper will be of great significance for the study of improving and developing complex analysis, integral equation, and boundary value theory.