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Bücher Wissen & Bildung Englische Bücher Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Theory of Reproducing Kernels and Applications
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Theory of Reproducing Kernels and Applications
Yoshihiro Sawano (Taschenbuch, Englisch)
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Beschreibung
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 Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory ofAkira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
22.04.2018
Sprache
Englisch
EAN
9789811091841
Herausgeber
Springer Singapore
Serien- oder Bandtitel
Developments in Mathematics
Sonderedition
Nein
Autor
Yoshihiro Sawano
Seitenanzahl
452
Auflage
Softcover reprint of the original 1st edition 2016
Einbandart
Taschenbuch
Schlagwörter
reproducing kernel, inverse problem, Hilbert space, operator equation, Tikhonov regularization (discretization), MSC: 30C40,44A05,35A22,30B40,45A05,41A50,46E22, partial differential equations
Thema-Inhalt
PBKF - Funktionalanalysis und Abwandlungen
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBKJ - Differentialrechnung und -gleichungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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