Discrete Orthogonal Polynomials. (AM-164)
| Author | : Jinho Baik |
| Publisher | : Princeton University Press |
| Total Pages | : 178 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0691127344 |
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Discrete Orthogonal Polynomials Am 164
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Discrete Orthogonal Polynomials. (AM-164)
| Author | : J. Baik |
| Publisher | : Princeton University Press |
| Total Pages | : 179 |
| Release | : 2007-01-02 |
| Genre | : Mathematics |
| ISBN | : 1400837138 |
This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
The Multiple Facets of Partial Least Squares and Related Methods
| Author | : Hervé Abdi |
| Publisher | : Springer |
| Total Pages | : 313 |
| Release | : 2016-10-13 |
| Genre | : Mathematics |
| ISBN | : 3319406434 |
This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics and practitioners. The selected chapters here highlight this diversity with applied examples as well as the most recent advances.
An Introduction to Orthogonal Polynomials
| Author | : Theodore S Chihara |
| Publisher | : Courier Corporation |
| Total Pages | : 276 |
| Release | : 2014-07-01 |
| Genre | : Mathematics |
| ISBN | : 0486141411 |
Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.
Special Functions
| Author | : Richard Beals |
| Publisher | : Cambridge University Press |
| Total Pages | : |
| Release | : 2010-08-12 |
| Genre | : Mathematics |
| ISBN | : 1139490435 |
The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
Random Matrix Theory, Interacting Particle Systems and Integrable Systems
| Author | : Percy Deift |
| Publisher | : Cambridge University Press |
| Total Pages | : 539 |
| Release | : 2014-12-15 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 1107079926 |
This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
Orthogonal Polynomials on the Unit Circle: Spectral theory
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 608 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9780821836750 |
Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
Engineering Applications of Noncommutative Harmonic Analysis
| Author | : Gregory S. Chirikjian |
| Publisher | : CRC Press |
| Total Pages | : 555 |
| Release | : 2021-02-25 |
| Genre | : Mathematics |
| ISBN | : 1000697339 |
First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
RF Imperfections in High-rate Wireless Systems
| Author | : Tim Schenk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 323 |
| Release | : 2008-01-29 |
| Genre | : Technology & Engineering |
| ISBN | : 1402069030 |
This is one of the first books on the emerging research topic of digital compensation of RF imperfections. The book presents a new multidisciplinary vision on the design of wireless communication systems. In this approach the imperfections of the RF front-ends are accepted and digital signal processing algorithms are designed to suppress their impact on system performance. The book focuses on multiple-antenna orthogonal frequency division multiplexing (MIMO OFDM).
Orthogonal Polynomials
| Author | : Gabor Szeg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 448 |
| Release | : 1939-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821810235 |
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.
