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Fourier series and orthogonal polynomials
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Dunham Jackson
This text illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Begins with a definition and explanation of the elements of Fourier series, and examines Legendre polynomials and Bessel functions. Also includes Pearson frequency functions and chapters on orthogonal, Jacobi, ...
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Chebyshev & Fourier Spectral Methods
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J P Boyd
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, spherical and ...
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Field Theory
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Steven Roman, PH.D.
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. ...
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Structured Matrices and Polynomials
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Victor Pan
Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. ...
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Polynomials
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Edward J Barbeau
The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and ...
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Polynomial Operator Equations in Abstract Spaces and Applications
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Ioannis Argyros, Aoannis K Argyros
Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of ...
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The Real Fatou Conjecture. (Am-144)
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Jacek Graczyk, Grzegorz Swiatek
In 1920, Pierre Fatou expressed the conjecture that - except for special cases - all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set ...
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Complex Dynamics and Renormalization
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Curtis T McMullen
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As ...
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Polynomial Convexity
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Edgar Lee Stout
This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. "Polynomial Convexity" presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. It motivates the ...
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Combinatorial Methods: Free Groups, Polynomials, and Free Algebras
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Vladimir Shpilrain, Alexander Mikhalev, Jie-Tai Yu
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology at the beginning of the 20th Century. This book is divided into ...
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Walsh Equiconvergence of Complex Interpolating Polynomials
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Amnon Jakimovski, Ambikeshwar Sharma, Jszsef Szabados
This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J. L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, ...
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Elliptic Polynomials
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John S Lomont, John Brillhart
A remarkable interplay exists between the fields of elliptic functions and orthogonal polynomials. In the first monograph to explore their connections, Elliptic Polynomials combines these two areas of study, leading to an interesting development of some basic aspects of each. It presents new material about various classes of polynomials and about ...
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Global Bifurcation Theory and Hilbert's Sixteenth Problem
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Valery A Gaiko
This volume is devoted to the qualitative investigation of two-dimensional polynomial dynamical systems, and is aimed at solving Hilbert's Sixteenth Problem on the maximum number and relative position of limit cycles. The author presents a global bifurcation theory of such systems and suggests a new global approach to the study of limit cycle ...
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Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
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Christian U Jensen, Arne Ledet, Noriko Yui
This book describes a constructive approach to the Inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme ...
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Orthogonal Polynomials and Continued Fractions: From Euler's Point of View
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Sergey Khrushchev
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions ...
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Positive Polynomials: From Hilbert's 17th Problem to Real Algebra
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Alexander Prestel, Charles N Delzell
Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations ...
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Effective Polynomial Computation
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Zippel
Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are ...
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Discrepancy of Signed Measures and Polynomial Approximation
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Vladimir V Andrievskii, Hans-Peter Blatt
The book is an authoritative and up-to-date introduction to the field of Analysis and Potential Theory dealing with the distribution of zeros of classical systems of polynomials such as orthogonal polynomials, Chebyshev, Fekete and Bieberbach polynomials, best or near-best approximating polynomials on compacts sets and on the real line. The main ...
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Double Affine Hecke Algebras
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Ivan Cherednik
This is a unique, essentially self-contained, monograph in a new field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is ...
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Degree of Approximation by Polynomials in the Complex Domain
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W. E. Sewell
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Local Polynomial Modelling and Its Applications: Monographs on Statistics and Applied Probability 66
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by
Jinqing Fan, Jianqing Fan, Irene Gijbels
Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with ...
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Orthogonal Polynomials for Exponential Weights
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by
A L Levin, Eli Levin, Doron S Lubinsky
The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in importance in the future.In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval ...
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Handbook of Computational Methods for Integration
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Michael R Schaferkotter, Prem K Kythe
During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open ...
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From Polynomials to Sums of Squares
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by
Terence H Jackson
"From Polynomials to Sums of Squares" describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is ...
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Orthogonal polynomials and their applications proceedings of the international congress
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Vinuesa
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