Topics in Polynomials: Extremal Problems, Inequalities, Zeros - Hardcover

Milovanovic, Gradimir V; Rassias, Themistocles M; Mitrinovic, D S

Hardcover

ISBN 10: 981020499X ISBN 13: 9789810204990

Publisher: World Scientific Publishing Co Pte Ltd, 1991

Synopsis

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.

About this title

Review

"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 fur Mathematik

Synopsis

This book contains results on the analysis of polynomials and their derivatives. It includes an extensive analysis of orthogonal polynomials as well as of trigonometric sums. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning external properties of polynomials in various metrics with an extensive analysis of inequalities for polynomials, and their derivatives as well as their zeros. 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.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 1991
• Language: English
• ISBN 10: 981020499X
• ISBN 13: 9789810204990
• Binding: Hardcover
• Number of pages: 836