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

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

Author | : Robert Gardner,Narendra Govil,Gradimir V. Milovanovic |

Publsiher | : Academic Press |

Total Pages | : 304 |

Release | : 2019-11-15 |

ISBN 10 | : 9780128119884 |

ISBN 13 | : 0128119888 |

Language | : EN, FR, DE, ES & NL |

**Extremal Problems and Inequalities of Markov Bernstein Type for Algebraic Polynomials Book Review:**

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

## Topics in Polynomials

Author | : G V Milovanovic,D S Mitrinovic,Th M Rassias |

Publsiher | : World Scientific |

Total Pages | : 836 |

Release | : 1994-06-28 |

ISBN 10 | : 9814506486 |

ISBN 13 | : 9789814506489 |

Language | : EN, FR, DE, ES & NL |

**Topics in Polynomials Book Review:**

The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution. Contents:PrefaceGeneral Concept of Algebraic PolynomialsSelected Polynomial InequalitiesZeros of PolynomialsInequalities Connected with Trigonometric SumsExtremal Problems for PolynomialsExtremal Problems of Markov-Bernstein TypeSome Applications of PolynomialsSymbol IndexName IndexSubject Index Readership: Mathematicians and mathematical physicists. keywords:Algebraic Polynomials;Trigonometric Polynomials;Zeros;Extremal Problems;Trigonometric Sums;Positivity and Monotonicity;Distribution of Zeros;Bounds for Polynomial Zeros;Incomplete Polynomials;Polynomials with Minimal Norm;Markov-Bernstein Inequalities;Approximation;Symmetric Functions;Orthogonal Polynomials;Nonnegative Polynomials “The topics are tastefully selected and the results are easy to find. Although this book is not really planned as a textbook to teach from, it is excellent for self-study or seminars. This is a very useful reference book with many results which have not appeared in a book form yet. It is an important addition to the literature.” Journal of Approximation Theory “I find the book to be well written and readable. The authors have made an attempt to present the material in an integrated and self-contained fashion and, in my opinion, they have been greatly successful. The book would be useful not only for the specialist mathematician, but also for those researchers in the applied and computational sciences who use polynomials as a tool.” Mathematical Reviews “This is a remarkable book, offering a cornucopia of results, all connected by their involvement with polynomials. The scope of the volume can be conveyed by citing some statistics: there are 821 pages, 7 chapters, 20 sections, 108 subsections, 95 pages of references (distributed throughout the book), a name index of 16 pages, and a subject index of 19 pages … The book is written in a gentle style: one can open it anywhere and begin to understand, without encountering unfamiliar notation and terminology. It is strongly recommended to individuals and to libraries.” Mathematics of Computation “This book contains some of the most important results on the analysis of polynomials and their derivatives … is intended, not only for the specialist mathematician, but also for those researchers in the applied sciences who use polynomials as a tool.” Sever S Dragomir “This is a well-written book on a widely useful topic. It is strongly recommended not only to the mathematical specialist, but also to all those researchers in the applied and computational sciences who make frequent use of polynomials as a tool. Of course, libraries will also benefit greatly by including this book in their cherished collection.” Mathematics Abstracts “There is no doubt that this is a very useful work compiling enormous researches carried out on the subject … This is a well-written book on a widely useful topic.” Zentralblatt für Mathematik

## Approximation Theory

Author | : Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados |

Publsiher | : CRC Press |

Total Pages | : 552 |

Release | : 2021-02-01 |

ISBN 10 | : 1000146030 |

ISBN 13 | : 9781000146035 |

Language | : EN, FR, DE, ES & NL |

**Approximation Theory Book Review:**

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

## Generalized Functions and Convergence

Author | : Piotr Antosik,Andrzej Kamiński |

Publsiher | : World Scientific Publishing Company Incorporated |

Total Pages | : 386 |

Release | : 1990 |

ISBN 10 | : |

ISBN 13 | : UCAL:B4406622 |

Language | : EN, FR, DE, ES & NL |

**Generalized Functions and Convergence Book Review:**

The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures.

## Mathematical Reviews

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2007 |

ISBN 10 | : |

ISBN 13 | : UOM:39015078588616 |

Language | : EN, FR, DE, ES & NL |

**Mathematical Reviews Book Review:**

## Journal of the Indian Institute of Science

Author | : Indian Institute of Science, Bangalore |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1997 |

ISBN 10 | : |

ISBN 13 | : UCSD:31822009135989 |

Language | : EN, FR, DE, ES & NL |

**Journal of the Indian Institute of Science Book Review:**

## Algebras Groups and Geometries

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1996 |

ISBN 10 | : |

ISBN 13 | : UOM:39015038957422 |

Language | : EN, FR, DE, ES & NL |

**Algebras Groups and Geometries Book Review:**

## General Inequalities 6

Author | : Wolfgang Walter |

Publsiher | : Birkhäuser |

Total Pages | : 508 |

Release | : 1992-04-10 |

ISBN 10 | : 9783764327378 |

ISBN 13 | : 3764327375 |

Language | : EN, FR, DE, ES & NL |

**General Inequalities 6 Book Review:**

The sixthInternational Conference on General Inequalities was held from Dec. 9 to Dec. 15, 1990, at the Mathematisches Forschungsinstitut Oberwolfach (Black Fa rest, Germany). The organizing committee was composed of W.N. Everitt (Birm ingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec ( Coimbra) served cheerfully and efficiently as secretary of the meeting. The con ference was attended by 44 participants from 20 countries. Yet again the importance of inequalities in both pure and applied mathematics was made evident from the wide range of interests of the individual participants, and from the wealth of new results announced. New inequalities were presented in the usual spread of the subject areas now expected for these meetings: Classical and functional analysis, existence and boundary value problems for both ordinary and partial differential equations, with special contributions to computer science, quantum holography and error analysis. More strongly than ever, the role played by modern electronic computers was made clear in testing out and prohing into the validity and structure of certain inequalities. Here the computer acts not only for numerical calculations of great complexity, but also in symbolic manipulation of complex finite structures. Prob lems in inequalities which even a few years ago were intractable, now fall to solution or receive direct and positive guidance as a result of computer applications. The interface between finite and infinite structures in mathematics and the versatility of modern computers is weil developed in the subject of general inequalities.

## Polynomials and Polynomial Inequalities

Author | : Peter Borwein,Tamas Erdelyi |

Publsiher | : Springer Science & Business Media |

Total Pages | : 480 |

Release | : 2012-12-06 |

ISBN 10 | : 1461207932 |

ISBN 13 | : 9781461207931 |

Language | : EN, FR, DE, ES & NL |

**Polynomials and Polynomial Inequalities Book Review:**

After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Müntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality round off the text. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis.

## Journal of Natural Geometry

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1994 |

ISBN 10 | : |

ISBN 13 | : UOM:39015046563980 |

Language | : EN, FR, DE, ES & NL |

**Journal of Natural Geometry Book Review:**

## Extremal Properties of Polynomials and Splines

Author | : Nikolaĭ Pavlovich Korneĭchuk,Anatoliĭ Aleksandrovich Ligun,V. F. Babenko |

Publsiher | : Nova Publishers |

Total Pages | : 433 |

Release | : 1996 |

ISBN 10 | : 9781560723615 |

ISBN 13 | : 1560723610 |

Language | : EN, FR, DE, ES & NL |

**Extremal Properties of Polynomials and Splines Book Review:**

Extremal Properties of Polynomials & Splines

## New Technical Books

Author | : New York Public Library |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1976 |

ISBN 10 | : |

ISBN 13 | : UOM:39015036923210 |

Language | : EN, FR, DE, ES & NL |

**New Technical Books Book Review:**

## Topics in Polynomials of One and Several Variables and Their Applications

Author | : Themistocles M. Rassias,H. M. Srivastava |

Publsiher | : World Scientific |

Total Pages | : 638 |

Release | : 1993 |

ISBN 10 | : 9789810206147 |

ISBN 13 | : 9810206143 |

Language | : EN, FR, DE, ES & NL |

**Topics in Polynomials of One and Several Variables and Their Applications Book Review:**

This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.

## Analytic Theory of Polynomials

Author | : Qazi Ibadur Rahman,Department of Mathematics and Statistics Qazi Ibadur Rahman,Gerhard Schmeisser |

Publsiher | : Oxford University Press |

Total Pages | : 742 |

Release | : 2002 |

ISBN 10 | : 9780198534938 |

ISBN 13 | : 0198534930 |

Language | : EN, FR, DE, ES & NL |

**Analytic Theory of Polynomials Book Review:**

Presents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.

## Approximation Theory II

Author | : G. G. Lorentz,Elliott W. Cheney,C. K. Chui,Larry L. Schumaker |

Publsiher | : Unknown |

Total Pages | : 588 |

Release | : 1976 |

ISBN 10 | : |

ISBN 13 | : UOM:39015046282151 |

Language | : EN, FR, DE, ES & NL |

**Approximation Theory II Book Review:**

The thief Parker teams up with some crooks to steal half a million dollars from a TV evangelist. But one cannot keep his mouth shut and Parker is on the run, pursued by people on both sides of the law.

## Approximation Theory

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1976 |

ISBN 10 | : |

ISBN 13 | : STANFORD:36105031824209 |

Language | : EN, FR, DE, ES & NL |

**Approximation Theory Book Review:**

## Journal of Contemporary Mathematical Analysis

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2001 |

ISBN 10 | : |

ISBN 13 | : UOM:39015059067135 |

Language | : EN, FR, DE, ES & NL |

**Journal of Contemporary Mathematical Analysis Book Review:**

## Constructive Approximation

Author | : George G. Lorentz,Manfred v. Golitschek,Yuly Makovoz |

Publsiher | : Springer |

Total Pages | : 649 |

Release | : 2011-12-21 |

ISBN 10 | : 9783642646102 |

ISBN 13 | : 3642646107 |

Language | : EN, FR, DE, ES & NL |

**Constructive Approximation Book Review:**

In the last 30 years, Approximation Theory has undergone wonderful develop ment, with many new theories appearing in this short interval. This book has its origin in the wish to adequately describe this development, in particular, to rewrite the short 1966 book of G. G. Lorentz, "Approximation of Functions." Soon after 1980, R. A. DeVore and Lorentz joined forces for this purpose. The outcome has been their "Constructive Approximation" (1993), volume 303 of this series. References to this book are given as, for example rCA, p.201]. Later, M. v. Golitschek and Y. Makovoz joined Lorentz to produce the present book, as a continuation of the first. Completeness has not been our goal. In some of the theories, our exposition offers a selection of important, representative theorems, some other cases are treated more systematically. As in the first book, we treat only approximation of functions of one real variable. Thus, functions of several variables, complex approximation or interpolation are not treated, although complex variable methods appear often.

## High Dimensional Probability

Author | : Roman Vershynin |

Publsiher | : Cambridge University Press |

Total Pages | : 296 |

Release | : 2018-09-27 |

ISBN 10 | : 1108415199 |

ISBN 13 | : 9781108415194 |

Language | : EN, FR, DE, ES & NL |

**High Dimensional Probability Book Review:**

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

## Proceedings of the ACM Symposium on Theory of Computing

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2002 |

ISBN 10 | : |

ISBN 13 | : UOM:39015048304615 |

Language | : EN, FR, DE, ES & NL |

**Proceedings of the ACM Symposium on Theory of Computing Book Review:**