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000763458 019__ $$a960902372$$a961007301$$a961154045$$a962436311
000763458 020__ $$a9789811005305$$q(electronic book)
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000763458 1001_ $$aSaitoh, Saburou,$$d1944-$$eauthor.
000763458 24510 $$aTheory of reproducing kernels and applications /$$cSaburou Saitoh, Yoshihiro Sawano.
000763458 264_1 $$aSingapore :$$bSpringer,$$c2016.
000763458 300__ $$a1 online resource.
000763458 336__ $$atext$$btxt$$2rdacontent
000763458 337__ $$acomputer$$bc$$2rdamedia
000763458 338__ $$aonline resource$$bcr$$2rdacarrier
000763458 4901_ $$aDevelopments in mathematics,$$x1389-2177 ;$$vvolume 44
000763458 504__ $$aIncludes bibliographical references and index.
000763458 5050_ $$aDefinitions and examples of reproducing kernel Hilbert spaces -- Fundamental properties of RKHS -- Moore Penrose generalized inverses and Tikhonov regularization -- Real inversion formulas of the Laplace transform -- Applications to ordinary differential equations -- Applications to partial differential equations -- Applications to integral equations -- Special topics on reproducing kernels -- Appendices -- Index.
000763458 506__ $$aAccess limited to authorized users.
000763458 520__ $$aThis 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, and as well, a general integral transform theory are introduced. In three Appendices, the deep theory of Akira 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.
000763458 588__ $$aDescription based on print version record.
000763458 650_0 $$aHilbert space.
000763458 650_0 $$aKernel functions.
000763458 7001_ $$aSawano, Yoshihiro,$$eauthor.
000763458 77608 $$iPrint version:$$aSaitoh, Saburou.$$tTheory of reproducing kernels and applications.$$d[Place of publication not identified] : Springer, 2016$$z981100529X$$w(OCoLC)933713966
000763458 830_0 $$aDevelopments in mathematics ;$$vv. 44.
000763458 852__ $$bebk
000763458 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-981-10-0530-5$$zOnline Access$$91397441.1
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