Approximation Theory Using Positive Linear Operators
Approximation Theory Using Positive Linear Operators

Author: Radu Paltanea

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 208

ISBN-13: 1461220580

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Offers an examination of the multivariate approximation case Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators Many general estimates, leaving room for future applications (e.g. the B-spline case) Extensions to approximation operators acting on spaces of vector functions Historical perspective in the form of previous significant results

Convergence Estimates in Approximation Theory
Convergence Estimates in Approximation Theory

Author: Vijay Gupta

Publisher: Springer Science & Business Media

Published: 2014-01-08

Total Pages: 368

ISBN-13: 3319027654

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The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive operators in real and complex domains. The theoretical aspects of these operators have been an active area of research over the past few decades. In this volume, authors Gupta and Agarwal explore new and more efficient methods of applying this research to studies in Optimization and Analysis. The text will be of interest to upper-level students seeking an introduction to the field and to researchers developing innovative approaches.

Recent Advances in Constructive Approximation Theory
Recent Advances in Constructive Approximation Theory

Author: Vijay Gupta

Publisher: Springer

Published: 2018-07-06

Total Pages: 295

ISBN-13: 3319921657

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This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.

Selected Topics in Complex Analysis
Selected Topics in Complex Analysis

Author: Vladimir Ya. Eiderman

Publisher: Springer Science & Business Media

Published: 2005-04-20

Total Pages: 240

ISBN-13: 9783764372514

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This volume opens with a paper by V.P. Havin that presents a comprehensive survey of the work of mathematician S.Ya. Khavinson. It includes a complete bibliography, previously unpublished, of 163 items, and twelve peer-reviewed research and expository papers by leading mathematicians, including the joint paper by Khavinson and T.S. Kuzina. The emphasis is on the usage of tools from functional analysis, potential theory, algebra, and topology.

Applications of q-Calculus in Operator Theory
Applications of q-Calculus in Operator Theory

Author: Ali Aral

Publisher: Springer Science & Business Media

Published: 2013-05-09

Total Pages: 275

ISBN-13: 1461469465

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The approximation of functions by linear positive operators is an important research topic in general mathematics and it also provides powerful tools to application areas such as computer-aided geometric design, numerical analysis, and solutions of differential equations. q-Calculus is a generalization of many subjects, such as hypergeometric series, complex analysis, and particle physics. ​​This monograph is an introduction to combining approximation theory and q-Calculus with applications, by using well- known operators. The presentation is systematic and the authors include a brief summary of the notations and basic definitions of q-calculus before delving into more advanced material. The many applications of q-calculus in the theory of approximation, especially on various operators, which includes convergence of operators to functions in real and complex domain​ forms the gist of the book. This book is suitable for researchers and students in mathematics, physics and engineering, and for professionals who would enjoy exploring the host of mathematical techniques and ideas that are collected and discussed in the book.

Computation and Approximation
Computation and Approximation

Author: Vijay Gupta

Publisher: Springer Nature

Published: 2021-11-29

Total Pages: 107

ISBN-13: 3030855635

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This brief studies recent work conducted on certain exponential type operators and other integral type operators. It consists of three chapters: the first on exponential type operators, the second a study of some modifications of linear positive operators, and the third on difference estimates between two operators. It will be of interest to students both graduate and undergraduate studying linear positive operators and the area of approximation theory.

Markov Operators, Positive Semigroups and Approximation Processes
Markov Operators, Positive Semigroups and Approximation Processes

Author: Francesco Altomare

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-12-17

Total Pages: 326

ISBN-13: 3110366975

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This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.

Moments of Linear Positive Operators and Approximation
Moments of Linear Positive Operators and Approximation

Author: Vijay Gupta

Publisher: Springer

Published: 2019-05-25

Total Pages: 102

ISBN-13: 3030194558

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This book is a valuable resource for Graduate students and researchers interested in current techniques and methods within the theory of moments in linear positive operators and approximation theory. Moments are essential to the convergence of a sequence of linear positive operators. Several methods are examined to determine moments including direct calculations, recurrence relations, and the application of hypergeometric series. A collection of operators in the theory of approximation are investigated through their moments and a variety of results are surveyed with fundamental theories and recent developments. Detailed examples are included to assist readers understand vital theories and potential applications.

Operator Theory, Operator Algebras, and Matrix Theory
Operator Theory, Operator Algebras, and Matrix Theory

Author: Carlos André

Publisher: Birkhäuser

Published: 2018-08-22

Total Pages: 381

ISBN-13: 3319724495

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This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.