Sampling of vector-valued transforms associated with solutions and Green’s matrix of discontinuous Dirac systems

Boundary value problems

Abdulaziz S Alofi¹  Mohammed M Tharwat² 

[1] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

关键词: Dirac systems;    transmission conditions;    eigenvalue parameter in the boundary conditions;    discontinuous boundary value problems;    34L16;    94A20;    65L15;   

DOI  :  10.1186/s13661-015-0290-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Our goal in the current paper is to derive the sampling theorems of a Dirac system with a spectral parameter appearing linearly in the boundary conditions and also with an internal point of discontinuity. To derive the sampling theorems including the construction of Green’s matrix as well as the eigenvector-function expansion theorem, we briefly study the spectral analysis of the problem as in Levitan and Sargsjan (Translations of Mathematical Monographs, vol. 39, 1975; Sturm-Liouville and Dirac Operators, 1991) in a way similar to that of Fulton (Proc. R. Soc. Edinb. A 77:293-308, 1977) and Kerimov (Differ. Equ. 38(2):164-174, 2002). We derive sampling representations for transforms whose kernels are either solutions or Green’s matrix of the problem. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in Annaby and Tharwat (J. Appl. Math. Comput. 36:291-317, 2011).

【 授权许可】

CC BY