Bernstein Functions

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Bernstein Functions

Author : René L. Schilling
Publisher : Walter de Gruyter
ISBN 13 : 3110269333
Total Pages : 424 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Bernstein Functions by : René L. Schilling

Download or read book Bernstein Functions written by René L. Schilling and published by Walter de Gruyter. This book was released on 2012-10-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis – often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'. This monograph – now in its second revised and extended edition – offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided.

Special Functions for Applied Scientists

Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 0387758941
Total Pages : 480 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Special Functions for Applied Scientists by : A.M. Mathai

Download or read book Special Functions for Applied Scientists written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2008-02-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.

Approximation By Complex Bernstein And Convolution Type Operators

Author : Sorin G Gal
Publisher : World Scientific
ISBN 13 : 9814466972
Total Pages : 350 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Approximation By Complex Bernstein And Convolution Type Operators by : Sorin G Gal

Download or read book Approximation By Complex Bernstein And Convolution Type Operators written by Sorin G Gal and published by World Scientific. This book was released on 2009-08-11 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.

Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials

Author : Robert B. Gardner
Publisher : Elsevier
ISBN 13 : 0128119888
Total Pages : 442 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials by : Robert B. Gardner

Download or read book Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials written by Robert B. Gardner and published by Elsevier. This book was released on 2022-02-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions Contains exhaustive references with thousands of citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research

Fourier Analysis and Approximation of Functions

Author : Roald M. Trigub
Publisher : Springer Science & Business Media
ISBN 13 : 9781402023415
Total Pages : 610 pages
Book Rating : 4.0/5 (234 download)

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Book Synopsis Fourier Analysis and Approximation of Functions by : Roald M. Trigub

Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.

Bernstein Operators and Their Properties

Author : Jorge Bustamante
Publisher : Birkhäuser
ISBN 13 : 3319554026
Total Pages : 423 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Bernstein Operators and Their Properties by : Jorge Bustamante

Download or read book Bernstein Operators and Their Properties written by Jorge Bustamante and published by Birkhäuser. This book was released on 2017-04-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.

Quasianalytic Functions in the Sense of Bernstein

Author : W. Pleśniak
Publisher :
ISBN 13 :
Total Pages : 74 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Quasianalytic Functions in the Sense of Bernstein by : W. Pleśniak

Download or read book Quasianalytic Functions in the Sense of Bernstein written by W. Pleśniak and published by . This book was released on 1977 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bernstein Polynomials

Author : G. G. Lorentz
Publisher : American Mathematical Soc.
ISBN 13 : 0821875582
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Bernstein Polynomials by : G. G. Lorentz

Download or read book Bernstein Polynomials written by G. G. Lorentz and published by American Mathematical Soc.. This book was released on 2012 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis. The first three chapters of the book give an introduction to a theory of singular integrals by means of the particular instance of Bernstein polynomials. The author writes in the preface to this second edition, "After the trigonometric integrals, Bernstein polynomials are the most important and interesting concrete operators on a space of continuous functions. Since the appearance of the first edition of this book [in 1953], the interest in this subject has continued. In an appendix we have summed up a few of the most important papers that have appeared since."

Nikolai Bernstein - from Reflex to the Model of the Future

Author : Josef M. Feigenberg
Publisher : LIT Verlag Münster
ISBN 13 : 3643905831
Total Pages : 269 pages
Book Rating : 4.6/5 (439 download)

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Book Synopsis Nikolai Bernstein - from Reflex to the Model of the Future by : Josef M. Feigenberg

Download or read book Nikolai Bernstein - from Reflex to the Model of the Future written by Josef M. Feigenberg and published by LIT Verlag Münster. This book was released on 2014 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nikolai Alexandrovich Bernstein (1896-1966) is regarded as one of the most prominent scientists in 20th-century physiology. As a skillful research scientist and a deep thinker, he laid the foundations for the contemporary biomechanics of human movements and theory of movement control. His contributions to the fields of neurophysiology are still highly valued by the international scientific community. This publication maintains and progresses Bernstein's heritage. (Series: Studies in Sports History / Studien zur Geschichte des Sports - Vol. 17) [Subject: Biography, Physiology, Science, History of Sport]

IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2

Author : Robin Bouclier
Publisher : John Wiley & Sons
ISBN 13 : 1394229623
Total Pages : 244 pages
Book Rating : 4.3/5 (942 download)

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Book Synopsis IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2 by : Robin Bouclier

Download or read book IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2 written by Robin Bouclier and published by John Wiley & Sons. This book was released on 2023-07-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, almost twenty years after its creation, substantial works are being reported in IGA, making it very competitive in scientific computing. This book proposes to use IGA jointly with standard finite element methods (FEM), presenting IGA as a projection of FEM on a more regular reduced basis. By shedding new light on how IGA relates to FEM, we can see how IGA can be implemented on top of an FE code in order to improve the solution of problems that require more regularity. This is illustrated by using IGA with FEM in a non-invasive fashion to perform efficient and robust multiscale global/local simulations in solid mechanics. Furthermore, we show that IGA can regularize the inverse problem of FE digital image correlation in experimental mechanics.

Operators, Semigroups, Algebras and Function Theory

Author : Yemon Choi
Publisher : Springer Nature
ISBN 13 : 3031380207
Total Pages : 262 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Operators, Semigroups, Algebras and Function Theory by : Yemon Choi

Download or read book Operators, Semigroups, Algebras and Function Theory written by Yemon Choi and published by Springer Nature. This book was released on 2023-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.

Bernstein's Construction of Movements

Author : Mark L. Latash
Publisher : Routledge
ISBN 13 : 1000213846
Total Pages : 379 pages
Book Rating : 4.0/5 (2 download)

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Book Synopsis Bernstein's Construction of Movements by : Mark L. Latash

Download or read book Bernstein's Construction of Movements written by Mark L. Latash and published by Routledge. This book was released on 2020-10-29 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nikolai Aleksandrovich Bernstein was one of the great neuroscientists of the twentieth century and highly respected by Western scientists even though most have never read his most important book entitled On the Construction of Movements. Bernstein's Construction of Movements: The Original Text and Commentaries is the first English translation. It supplements the translated text with a series of commentaries by scientists who knew Bernstein personally, as well as leaders in related fields including physics, motor control, and biomechanics. While written in 1947, Bernstein’s book is anything but obsolete, making this English translation and accompanying commentaries an invaluable text. The translated original text presents in detail Bernstein’s views on the evolutionary history of biological movement and his multi-level hierarchical scheme of the construction of movements in higher animals, including humans. The following commentaries address Bernstein’s personality, the history of the book, and current views on different aspects of neuroscience covered in Bernstein’s text. Ultimately, they present "a book within the book" to showcase how Bernstein’s heritage has developed over the past years. This classic, available for the first time to an English-speaking audience, will prove beneficial to students, instructors, and experts of neuroscience, physics, neurophysiology, motor control, motor rehabilitation, biomechanics, dynamical systems, and related fields.

Prologue

Author :
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Prologue by :

Download or read book Prologue written by and published by . This book was released on 1999 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Craft of Fractional Modelling in Science and Engineering

Author : Jordan Hristov
Publisher : MDPI
ISBN 13 : 303842983X
Total Pages : 139 pages
Book Rating : 4.0/5 (384 download)

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Book Synopsis The Craft of Fractional Modelling in Science and Engineering by : Jordan Hristov

Download or read book The Craft of Fractional Modelling in Science and Engineering written by Jordan Hristov and published by MDPI. This book was released on 2018-06-22 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "The Craft of Fractional Modelling in Science and Engineering" that was published in Fractal Fract

Basic Theory

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110570637
Total Pages : 683 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Basic Theory by : Anatoly Kochubei

Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Scalar, Vector, and Matrix Mathematics

Author : Dennis S. Bernstein
Publisher : Princeton University Press
ISBN 13 : 0691176531
Total Pages : 1593 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Scalar, Vector, and Matrix Mathematics by : Dennis S. Bernstein

Download or read book Scalar, Vector, and Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2018-02-27 with total page 1593 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index

Matrix Mathematics

Author : Dennis S. Bernstein
Publisher : Princeton University Press
ISBN 13 : 0691140391
Total Pages : 1183 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Matrix Mathematics by : Dennis S. Bernstein

Download or read book Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2009-07-26 with total page 1183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks.