Inzell Lectures On Orthogonal Polynomials
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Inzell Lectures On Orthogonal Polynomials
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Author : Wolfgang zu Castell
language : en
Publisher: Nova Publishers
Release Date : 2005
Inzell Lectures On Orthogonal Polynomials written by Wolfgang zu Castell and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Based on the success of Fourier analysis and Hilbert space theory, orthogonal expansions undoubtedly count as fundamental concepts of mathematical analysis. Along with the need for highly involved functions systems having special properties and analysis on more complicated domains, harmonic analysis has steadily increased its importance in modern mathematical analysis. Deep connections between harmonic analysis and the theory of special functions have been discovered comparatively late, but since then have been exploited in many directions. The Inzell Lectures focus on the interrelation between orthogonal polynomials and harmonic analysis.
Coimbra Lecture Notes On Orthogonal Polynomials
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Author : Amilcar Jose Pinto Lopes Branquinho
language : en
Publisher: Nova Publishers
Release Date : 2008
Coimbra Lecture Notes On Orthogonal Polynomials written by Amilcar Jose Pinto Lopes Branquinho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the most important deferential equations of mathematical physics. Hermite-Padé approximation was also introduced at that time, to prove the transcendence of the remarkable constant e (the basis of the natural logarithm). Since then OPSF has developed to a standard subject within mathematics, which is driven by applications. The applications are numerous, both within mathematics (e.g. statistics, combinatory, harmonic analysis, number theory) and other sciences, such as physics, biology, computer science, chemistry. The main reason for the fact that OPSF has been so successful over the centuries is its usefulness in other branches of mathematics and physics, as well as other sciences. There are many different aspects of OPSF. Some of the most important developments for OPSF are related to the theory of rational approximation of analytic functions, in particular the extension to simultaneous rational approximation to a system of functions. Important tools for rational approximation are Riemann-Hilbert problems, the theory of orthogonal polynomials, logarithmic potential theory, and operator theory for difference operators. This new book presents the latest research in the field.
Orthogonal Polynomials And Special Functions
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Author : Francisco Marcellàn
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-19
Orthogonal Polynomials And Special Functions written by Francisco Marcellàn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-19 with Mathematics categories.
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.
Advances In Underwater Acoustics Structural Acoustics And Computational Methodologies In 4 Volumes
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Author : Sean F Wu
language : en
Publisher: World Scientific
Release Date : 2025-04-29
Advances In Underwater Acoustics Structural Acoustics And Computational Methodologies In 4 Volumes written by Sean F Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-29 with Technology & Engineering categories.
This set of volumes encompasses the study of acoustics to diverse environments ranging from underwater and marine environments, to structural and civil engineering, computational models and aerospace engineering. Each volume comprises peer-reviewed publications in the related field of acoustics from the past decade, arranged such as to review the existing literature, examine new methodologies and then explore novel applications of pioneering acoustic principles. With contributions by eminent acoustics researchers, this set holds key insights for fellow acoustics researchers and engineers of any field impacted by acoustic phenomena.Volume 1's review chapters summarise theories like geoacoustic inversion as well as criticism of the Biot theory of propagation in fluid-saturated porous solids, while the new methodologies shown range from an efficient and stable coupled-mode solution to a cell-based smoothed radial point interpolation method. The book concludes with promising applications like experimental evidence of horizontal refraction and bottom attenuation coefficient inversion.Volume 2 reviews topics including radiation boundary conditions for the Helmholtz equation, and analytical interpretation of the early literature on the theory of vibrations. The methodologies range from coupled boundary element and energy flow method as well as sound radiation of a line source. The work concludes with promising applications like Lamb Waves in a poroelastic plate and experimental validations of reconstructed excitation forces acting inside a solid enclosure.Volume 3 provides summaries of theories including the benchmark study on eigenfrequencies of fluid-loaded structures, and the Burton and Miller method, while the new methodologies presented range from a coupled boundary element and energy flow method, to an efficient approach to the simulation of acoustic radiation. The volume concludes with promising applications like a comparison of transient infinite elements and transient Kirchhoff integral methods, as well as a fast multi-frequency iterative acoustic boundary element method.Volume 4 depicts the context of conventional methodologies including short-wave components and Galbrun's equation, while its new methodologies range from radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances to the effect of airfoil shape on trailing edge noise. The collection concludes with promising applications like helicopter noise predictions and conservative source interpolation methods for aeroacoustics.
Functional Equations On Hypergroups
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Author : L szl¢ Szkelyhidi
language : en
Publisher: World Scientific
Release Date : 2013
Functional Equations On Hypergroups written by L szl¢ Szkelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate OC marriageOCO where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods OCo and, sometimes, a new world of unexpected difficulties.
Laredo Lectures On Orthogonal Polynomials And Special Functions
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Author : Renato Alvarez-Nodarse
language : en
Publisher: Nova Publishers
Release Date : 2004
Laredo Lectures On Orthogonal Polynomials And Special Functions written by Renato Alvarez-Nodarse and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Structural Aspects In The Theory Of Probability
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Author : Herbert Heyer
language : en
Publisher: World Scientific
Release Date : 2010
Structural Aspects In The Theory Of Probability written by Herbert Heyer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Recent Advances In Orthogonal Polynomials Special Functions And Their Applications
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Author : Jorge Arves
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-09-11
Recent Advances In Orthogonal Polynomials Special Functions And Their Applications written by Jorge Arves and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.
Orthogonal Polynomials And Special Functions
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Author : Erik Koelink
language : en
Publisher: Springer
Release Date : 2003-07-03
Orthogonal Polynomials And Special Functions written by Erik Koelink and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.
The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.