Theory of Reproducing Kernels and Applications. 1st ed. 2016

種類:

電子ブック

責任表示:

by Saburou Saitoh, Yoshihiro Sawano

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2016

著者名:

• Saitoh, Saburou.
• Sawano, Yoshihiro.
• SpringerLink (Online service)

シリーズ名:

Developments in Mathematics ; 44

ISBN:

9789811005305 [9811005303]    

注記:

Definitions and examples of reproducing kernel Hilbert spaces -- Fundamental properties of RKHS -- Moore Penrose generalized inverses and Tikhonov regularization -- Real inversion formulas of the Laplace transform -- Applications to ordinary differential equations -- Applications to partial differential equations -- Applications to integral equations -- Special topics on reproducing kernels -- Appendices -- Index.
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications. In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book. Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations. In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results. Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapt

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