zbMATH — the first resource for mathematics

The exact solution of system of linear operator equations in reproducing kernel spaces. (English) Zbl 1163.47003
The authors discuss the problem of obtaining the exact and approximate solution of a system of linear operator equations in Hilbert spaces, including the special case of reproducing kernel spaces. They give some examples and discuss the results of a numerical experiment which shows the efficiency of the suggested methods.

MSC:
 47A50 Equations and inequalities involving linear operators, with vector unknowns 47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
Full Text:
References:
 [1] Bougoffa, L., Adomain method for a class of hyperbolic equations with an integral condition, Appl. math. comput., 177, 2, 545-552, (2006) · Zbl 1096.65102 [2] Cui, M.G.; Deng, Z.X., Best approximate interpolation operator in space $$W_2^1$$, J. comput. math., 2, 209-216, (1986) [3] Li, C.L.; Cui, M.G., The exact solution for solving a class nonlinear operator equation in the reproducing kernel space, Appl. math. comput., 143, 2-3, 393-399, (2003) · Zbl 1034.47030 [4] Aronszajn, N., Theory of reproducing kernels, Trans. AMS, 68, 337-404, (1950) · Zbl 0037.20701 [5] Cahlon, B.; Kulkarni, D.M.; Shi, P., Stepwise stability for the heat equation with a nonlocal constraint, SIAM J. numer. anal., 32, 571-593, (1995) · Zbl 0831.65094 [6] Choi, Y.S.; Chan, K.Y., A parabolic equation with nonlocal boundary conditions arising from electrochemistry, Nonlinear anal., 18, 317-331, (1992) · Zbl 0757.35031 [7] Belin, S.A., Existence of solutions for one-dimensional wave equations with nonlocal conditions, Electron. J. differ. equ., 76, 1-8, (2001) [8] Pulkina, L.S., A nonlocal problem with integral conditions for hyperbolic equations, Electron. J. differ. equ., 45, 1-6, (1999) · Zbl 0935.35027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.