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

ISBN-13: 9780128119884 / Angielski / Miękka / 2022 / 304 str.

Robert Gardner; Narendra Govil; Ram Mohapatra

Opis

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

Recenzje

"The book devotes sections to other types of inequalities concerning growth of polynomials, orthogonal polynomials and more." --MathSciNet.

Spis treści

1. History and Introduction of Markov and Bernstein Inequalities 2. Bernstein-Type Inequalities for Polynomials with Restricted Zero 3. Bernstein-Type Inequalities in ????????Norm 4. Bernstein-Type Inequalities for Polar Derivatives of Polynomials 5. Bernstein-Type Inequalities for Rational Functions 6. Bernstein-Type Inequalities for Entire Functions of Exponential Type

O autorze

Robert Gardner is a tenured Professor of Mathematics and Statistics at East Tennessee State University specializing in Bernstein-type inequalities. He has co-authored/co-edited two books, including Real Analysis with an Introduction to Wavelets and Applications that was published by Elsevier in 2005. Narendra K. Govil is Professor Emeritus in the Department of Mathematics and Statistics at Auburn University, from where he retired as Professor, in 2020. He received his M.Sc. from Aligarh Muslim University, India and Ph.D. from the University of Montreal, Canada. He is a Fellow of the National Academy of Sciences, India and has been Alumni Professor in Department of Mathematics and Statistics at Auburn University. Before joining Auburn in 1983, he was a Professor at Indian Institute of Technology (IIT), New Delhi, India. He is a researcher in Complex Analysis and Approximation Theory, and has written a large number of papers in subjects related to Bernstein-type Inequalities, Geometry of the Zeros of Polynomials, Special Functions, and Wavelets. He is presently serving as Editor/Associate Editor of several journals, and has co-authored/co-edited six books including Progress in Approximation Theory and Applicable Complex Analysis, published by Springer in 2017. Gradimir V. Milovanovic is a Professor of Numerical Analysis and Approximation Theory and Full Member of the Serbian Academy of Sciences and Arts. He studied at University of Nis, obtaining a B.Sc. (1971) in electrical engineering and computer sciences and an M.Sc. (1974) and a Ph.D. (1976) in mathematics.

He was with the Faculty of Electronic Engineering and the Department of Mathematics at the same place as, promoted to professor (1986) and acting as Dean of the Faculty of Electronic Engineering (2002-2004) and Rector of the University of Nis (2004-06), as well as Dean of the Faculty of Computer Sciences at the Megatrend University, Belgrade (2008-2011), until he joined the Mathematical Institute of the Serbian Academy of Sciences and Arts in Belgrade (2011). He was President of the National Council for Scientific and Technological Development of the Republic of Serbia (2006-2010).

His research interests are Orthogonal Polynomials and Systems; Interpolation, Quadrature Processes and Integral Equations; Approximation by Polynomials and Splines; Extremal Problems, Inequalities and Zeros of Polynomials. He published 7 monographs, about 250 scientific papers in refereed journals, 35 book chapters, about 50 papers in conference proceedings, as well as 20 textbooks. Most significant monograph works of Milovanovic are Topics in Polynomials: Extremal Problems, Inequalities, Zeros (coauthors: D. S. Mitrinovic and Th. M. Rassias), published at over 800 pages by World Scientific (Singapore, 1994) and known in the world as "Bible of Polynomials" and the monograph Interpolation Processes - Basic Theory and Applications (c??uthor: G. Mastroianni) by Springer, 2008. (Home page: http://www.mi.sanu.ac.rs/~gvm/ ). He is currently serving as an Editor-in-Chief and an Associate Editor for several journals (Journal of Inequalities and Applications, Springer; Optimization Letters, Springer; Applied Mathematics and Computation, Elsevier; Publications de l'Institut Mathématique, Mathematical Institute, Belgrade, etc.).