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Transformations Transmutations And Kernel Functions Volume Ii
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Book Synopsis Transformations, Transmutations, and Kernel Functions, Volume II by : H Begehr
Download or read book Transformations, Transmutations, and Kernel Functions, Volume II written by H Begehr and published by CRC Press. This book was released on 2023-06-16 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Book Synopsis Transformations, Transmutations, and Kernel Functions by : H Begehr
Download or read book Transformations, Transmutations, and Kernel Functions written by H Begehr and published by CRC Press. This book was released on 1993-09-23 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Book Synopsis Transmutation Operators and Applications by : Vladislav V. Kravchenko
Download or read book Transmutation Operators and Applications written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-04-11 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.
Book Synopsis Integral Transforms, Reproducing Kernels and Their Applications by : Saburou Saitoh
Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Reproducing Kernels and Applications by : Saburou Saitoh
Download or read book Theory of Reproducing Kernels and Applications written by Saburou Saitoh and published by Springer. This book was released on 2016-10-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.
Book Synopsis Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics by : Elina Shishkina
Download or read book Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina and published by Academic Press. This book was released on 2020-07-24 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. - Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods - Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details - Enables researchers, lecturers and students to find material under the single "roof"
Book Synopsis Analysis as a Life by : Sergei Rogosin
Download or read book Analysis as a Life written by Sergei Rogosin and published by Springer. This book was released on 2019-01-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).
Book Synopsis Direct and Inverse Sturm-Liouville Problems by : Vladislav V. Kravchenko
Download or read book Direct and Inverse Sturm-Liouville Problems written by Vladislav V. Kravchenko and published by Springer Nature. This book was released on 2020-07-28 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Book Synopsis Transformations, Transmutations, and Kernel Functions by : H Begehr
Download or read book Transformations, Transmutations, and Kernel Functions written by H Begehr and published by CRC Press. This book was released on 2019-12-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Book Synopsis Handbook of Complex Analysis by : Reiner Kuhnau
Download or read book Handbook of Complex Analysis written by Reiner Kuhnau and published by Elsevier. This book was released on 2004-12-09 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Book Synopsis Wavefield Inversion by : Armand Wirgin
Download or read book Wavefield Inversion written by Armand Wirgin and published by Springer. This book was released on 2014-05-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date presentation of a broad range of contemporary problems in inverse scattering involving acoustic, elastic and electromagnetic waves. Descriptions will be given of traditional (but still in use and subject to on-going improvements) and more recent methods for identifying either: a) the homogenized material parameters of (spatially) unbounded or bounded heterogeneous media, or b) the detailed composition (spatial distribution of the material parameters) of unbounded or bounded heterogeneous media, or c) the location, shape, orientation and material characteristics of an object embedded in a wellcharacterized homogeneous, homogenized or heterogeneous unbounded or bounded medium, by inversion of reflected, transmitted or scattered spatiotemporal recorded waveforms resulting from the propagation of probe radiation within the medium.
Book Synopsis Inverse Problems and Spectral Theory by : Hiroshi Isozaki
Download or read book Inverse Problems and Spectral Theory written by Hiroshi Isozaki and published by American Mathematical Soc.. This book was released on 2004 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
Book Synopsis Small Modifications of Quadrature Domains by : Makoto Sakai
Download or read book Small Modifications of Quadrature Domains written by Makoto Sakai and published by American Mathematical Soc.. This book was released on 2010 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.
Book Synopsis Analysis and Topology by : Simion Stoilow
Download or read book Analysis and Topology written by Simion Stoilow and published by World Scientific. This book was released on 1998 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow.
Book Synopsis Operator Theory for Complex and Hypercomplex Analysis by : Enrique Ramírez de Arellano
Download or read book Operator Theory for Complex and Hypercomplex Analysis written by Enrique Ramírez de Arellano and published by American Mathematical Soc.. This book was released on 1998 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers on certain aspects of general operator theory related to classes of important operators: singular integral, Toeplitz and Bergman opertors, convolution operators on Lie groups, pseudodifferential operators, etc. The study of these operators arises from integral representations for different classes of functions, enriches pure opertor theory, and is influential and beneficial for important areas of analysis. Particular attention is paid to the fruitful interplay of recent developments of complex and hypercomplex analysis on one side and to operator theory on the other. The majority of papers illustrate this interplay as well as related applications. The papers represent the proceedings of the conference "Operator Theory and Complex and Hypercomplex Analysis", held in Decenber 1994 in Mexico City.
Book Synopsis Complex Methods for Partial Differential Equations by : Heinrich Begehr
Download or read book Complex Methods for Partial Differential Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also by the proceedings in this ISAAC series and the ISAAC congresses and workshops.
Book Synopsis New Trends in Analysis and Interdisciplinary Applications by : Pei Dang
Download or read book New Trends in Analysis and Interdisciplinary Applications written by Pei Dang and published by Birkhäuser. This book was released on 2017-04-18 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers from the 10th ISAAC Congress 2015, held in Macau, China. The papers, prepared by respected international experts, address recent results in Mathematics, with a special focus on Analysis. By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.
