Contents: The Binomial Theorem in the Algebra A+ (L V Ahlfors)The Problem of the Local Solvability of the Linear Partial Differential Equations (A Corli & L Rodino)Entropy and Curvature (J Donato)Infinite-Dimensional Stochastic Differential Geometry in Modern Lagrangian Approach to Hydrodynamics of Viscous Incompressible Fluid (Y E Gliklikh)Application of C. Carathéodory's Theorem to a Problem of the Theory of Entire Functions (A A Gol'dberg)Simply Connected Domains with Finite Logarithmic Area and Riemann Mapping Functions (A Z Grinshpan & I M Milin)Systems Development Simulation Problems and C. Carathéodory's Concepts (V V Ivanov)On the Complex Analysis Methods for Some Classes of Partial Differential Equations (L G Mikhailov)Ordered Groups, Commuting Matrices and Iterations of Functions in Transformations of Differential Equations (F Neuman)The Isoperimetric Inequality and Eigenvalues of the Laplacian (Th M Rassias)Quasidirect Product Groups and the Lorentz Transformation Group (A A Ungar)and other papers
Contents:On the Characterization of Chebyshev Systems and on Conditions of Their Extension (Y G Abakumov)On Lagrange Polynomial Quasi-Interpolation (C K Chui et al.)The Convexity of Chebyshev Sets in Hilbert Space (F Deutsch)On the Completeness of Orthogonal Polynomials in Left-Definite Sobolev Spaces (W N Everitt et al.)A New Method for Generating Infinite Sets of Related Sequences of Orthogonal Polynomials, Starting from First-Order Initial-Value Problems (C C Grosjean)Orthogonal Polynomials on n-Spheres: Gegenbauer, Jacobi and Heun (E G Kalnins & W Miller, Jr)Extremal Problems for Polynomials and Their Coefficients (G V Milovanovi et al.)Some Recent Advances in the Theory of the Zeros and Critical Points of a Polynomial (Th M Rassias & H M Srivastava)Artificial Intelligence Today (G C Rota)A Certain Family of Generating Functions for Classical Orthogonal Polynomials (H M Srivastava)Mean Number of Real Zeros of a Random Trigonometric Polynomial. II (J E Wilkins, Jr)Orthogonal Polynomials of Many Variables and Degenerated Elliptic Equations (A Yanushauskas)and other papers
Readership: Mathematicians and mathematical physicists.
keywords:Polynomial Inequalities;Chebyshev Polynomials;Approximation Theory;Fourier Series;Special Functions;Lagrange Polynomials;Markov, Sobolev and Bernstein Inequalities;Orthogonal Polynomials;Generating Functions;Holographic Neural Networks;Integral Equations;Integral Transforms;Rational Approximations;Elliptic Equations;Sobolev Spaces
Contents:Symmetric Second Differences in Product form on Groups (J Aczél et al.)The Linear and Nonlinear Cauchy-Poisson Wave Problems for an Inviscid or Viscous Liquid (L Debnath)On the Representation of Functionals and the Stability of Mappings in Hilbert and Banach Space (H Drljevic)q-Extensions of Barnes', Cauchy's and Euler's Beta Integrals (G Gasper)Homology Groups, Differential Forms and Hecke Rings on Siegel Modular Varieties (K Hatada)A Representation of the Solution of the Cauchy's Problem for a Degenerate Hyperbolic Equation in Several Independent Variables (X Ji & D Chen)Nonnegativity of Mass and Entropy in Continous Dynamics (B A Kupershmidt)Regularity Theory for a Class of Non-Homogeneous Euler-Bernoulli Equations: A Cosine Operator Approach (I Lasiecka & R Triggiani)An Application of the Cauchy-Kowalewsky Theorem: The Minimal Surface Equation at Corners (H Parks)Martin Compactification for a Shrödinger Equation in an Angular Domain (T Tada)Non-Fredholm Boundary-value Problems for Multi-Dimensional Elliptic Equations (A Yanushauskas)Nonlocal Cauchy-Goursat Problem (V Zhegalov & R Chabakaev)On Certain Properties of Polynomials and Their Derivative (Th M Rassias)On Characterizations of Inner Product Spaces and Generalizations of the H Bohr Inequality (Th M Rassias)and other papers
Keywords:Mathematical Analysis;Cauchy;Nonlinear Cauchy-Poisson Wave Problems;Euler's Beta Integrals;Shrodinger;Polynomials
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