Linear Integral Equations

Ön Kapak
Springer Science & Business Media, 6 Ara 2012 - 367 sayfa
In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me. Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book. As in the first edition, the main motivation is to present the fundamental theory of integral equations, some of their main applications, and the basic concepts of their numerical solution in a single volume. This is done from my own perspective of integral equations; I have made no attempt to include all of the recent developments. In addition to making corrections and adjustments throughout the text and updating the references, the following topics have been added: In Sec tion 4.3 the presentation of the Fredholm alternative in dual systems has been slightly simplified and in Section 5.3 the short presentation on the index of operators has been extended. The treatment of boundary value problems in potential theory now includes proofs of the jump relations for single-and double-layer potentials in Section 6.3 and the solution of the Dirichlet problem for the exterior of an arc in two dimensions (Section 7.6). The numerical analysis of the boundary integral equations in Sobolev space settings has been extended for both integral equations of the first kind in Section 13.4 and integral equations of the second kind in Section 12.4.
 

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İçindekiler

Normed Spaces
1
Bounded and Compact Operators
15
Riesz Theory
28
Regularization in Dual Systems
55
Problems
66
Problems
92
Problems
124
Problems
151
Quadrature Methods
197
Projection Methods
218
Iterative Solution and Stability
247
Equations of the First Kind
265
Tikhonov Regularization
290
Regularization by Discretization
308
Inverse Boundary Value Problems
320
References
347

Problems
162
Degenerate Kernel Approximation
177

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