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Perturbations Of Fourier Series Of Orthogonal Polynomials
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Book Synopsis Fourier Series In Orthogonal Polynomials by : Boris Osilenker
Download or read book Fourier Series In Orthogonal Polynomials written by Boris Osilenker and published by World Scientific. This book was released on 1999-04-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic course on general orthogonal polynomials and Fourier series in orthogonal polynomials. It consists of six chapters. Chapter 1 deals in essence with standard results from the university course on the function theory of a real variable and on functional analysis. Chapter 2 contains the classical results about the orthogonal polynomials (some properties, classical Jacobi polynomials and the criteria of boundedness).The main subject of the book is Fourier series in general orthogonal polynomials. Chapters 3 and 4 are devoted to some results in this topic (classical results about convergence and summability of Fourier series in L2μ; summability almost everywhere by the Cesaro means and the Poisson-Abel method for Fourier polynomial series are the subject of Chapters 4 and 5).The last chapter contains some estimates regarding the generalized shift operator and the generalized product formula, associated with general orthogonal polynomials.The starting point of the technique in Chapters 4 and 5 is the representations of bilinear and trilinear forms obtained by the author. The results obtained in these two chapters are new ones.Chapters 2 and 3 (and part of Chapter 1) will be useful to postgraduate students, and one can choose them for treatment.This book is intended for researchers (mathematicians, mechanicians and physicists) whose work involves function theory, functional analysis, harmonic analysis and approximation theory.
Book Synopsis Laredo Lectures on Orthogonal Polynomials and Special Functions by : Renato Alvarez-Nodarse
Download or read book Laredo Lectures on Orthogonal Polynomials and Special Functions written by Renato Alvarez-Nodarse and published by Nova Publishers. This book was released on 2004 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.
Book Synopsis Perturbation Methods in Science and Engineering by : Reza N. Jazar
Download or read book Perturbation Methods in Science and Engineering written by Reza N. Jazar and published by Springer Nature. This book was released on 2021-07-12 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.
Book Synopsis Orthogonal Polynomials by : Gabor Szeg
Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.
Book Synopsis Orthogonal Polynomials in Two Variables by : P. K. Suetin
Download or read book Orthogonal Polynomials in Two Variables written by P. K. Suetin and published by CRC Press. This book was released on 1999-08-19 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Book Synopsis Szegő's Theorem and Its Descendants by : Barry Simon
Download or read book Szegő's Theorem and Its Descendants written by Barry Simon and published by Princeton University Press. This book was released on 2010-11-08 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
Book Synopsis Advanced Mathematical Methods with Maple by : Derek Richards
Download or read book Advanced Mathematical Methods with Maple written by Derek Richards and published by Cambridge University Press. This book was released on 2002 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: A user-friendly student guide to computer-assisted algebra with mathematical software packages such as Maple.
Book Synopsis Advanced Functional Analysis by : Eberhard Malkowsky
Download or read book Advanced Functional Analysis written by Eberhard Malkowsky and published by CRC Press. This book was released on 2019-02-25 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research
Book Synopsis Ordinary and Partial Differential Equations by : Ravi P. Agarwal
Download or read book Ordinary and Partial Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
Book Synopsis From Algebraic Structures to Tensors by : Gérard Favier
Download or read book From Algebraic Structures to Tensors written by Gérard Favier and published by John Wiley & Sons. This book was released on 2020-01-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order.
Book Synopsis An Operator Identity by : Glen E. Baxter
Download or read book An Operator Identity written by Glen E. Baxter and published by . This book was released on 1957 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let M be a matrix, Let M+ be formed by setting equal to zero all elements of M on or below the diagonal, and Let M- = M - M+. Equations P = I + s(MP)+ and Q = I + s(QM)- are investigated and their solutions applied to certain problems in the theory of probability where M is the transition probability matrix of a Markov chain. Extension to certain operators M is carried through.
Book Synopsis Classical and Quantum Orthogonal Polynomials in One Variable by : Mourad Ismail
Download or read book Classical and Quantum Orthogonal Polynomials in One Variable written by Mourad Ismail and published by Cambridge University Press. This book was released on 2005-11-21 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Download or read book Operator Theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.
Book Synopsis Mathematical Analysis of Physical Problems by : Philip Russell Wallace
Download or read book Mathematical Analysis of Physical Problems written by Philip Russell Wallace and published by Courier Corporation. This book was released on 1984-01-01 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.
Download or read book NASA Technical Memorandum written by and published by . This book was released on 1974 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularly Perturbed Methods for Nonlinear Elliptic Problems by : Daomin Cao
Download or read book Singularly Perturbed Methods for Nonlinear Elliptic Problems written by Daomin Cao and published by Cambridge University Press. This book was released on 2021-02-18 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to the singularly perturbed methods in the study of concentration solutions for nonlinear elliptic problems.
