Muutke küpsiste eelistusi

Integral Transforms, Reproducing Kernels and Their Applications [Kõva köide]

(Gunma University, Kiryu, Japan)
Teised raamatud teemal:
Integral Transforms, Reproducing Kernels and Their ApplicationsSuurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780582317581.html
Märksõnad:
The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Preface
Acknowledgments
1. Introduction
1(19)
2. Reproducing kernel Hilbert spaces
20(77)
1 Fundamental theorems of linear transforms
20(14)
2 Elementary properties of reproducing kernel Hilbert spaces
34(9)
3 Generations of reproducing kernel Hilbert spaces
43(10)
4 Examples of reproducing kernels
53(34)
5 Realizations of reproducing kernel Hilbert spaces
87(10)
3. Isometrical identities and inversion formulas
97(81)
1 Laplace and Fourier transforms
97(31)
2 The heat equation
128(15)
3 The wave equation
143(11)
4 Analytic and harmonic functions of class L(2)
154(14)
5 The Meyer wavelets
168(10)
4. Applications to the approximation of functions
178(22)
1 Best approximations by the functions in a RKHS
178(11)
2 Approximations in reproducing kernel Hilbert spaces
189(11)
5. Applications to analytic extension formulas and real inversion formulas for the Laplace transform
200(18)
1 Representations of the norms in Bergman-Selberg spaces
200(11)
2 Real inversion formulas for the Laplace transform
211(7)
6. Applications to source inverse problems
218(19)
1 Inverse source formulas in Poisson's equation
218(11)
2 Inverse source formulas for Helmholtz's equation
229(8)
Appendix
1. Applications to representations of inverse functions
237(6)
1 A general approach
237(2)
2 Reasonable settings
239(1)
3 Examples
240(3)
Appendix
2. Natural norm inequalities in nonlinear transforms
243(16)
1 General principles
243(5)
2 Concrete examples
248(11)
Appendix
3. Stability of Lipschitz type in determination of initial heat distribution
259(8)
1 Introduction and theorem
259(3)
2 Proof of theorem
262(5)
References 267(1)
Books 267(5)
Articles 272


Saitoh\, Saburou