Total Positivity and Its Applications

ISBN-13: 9789048146673 / Angielski / Miękka / 2010 / 518 str.

Mariano Gasca; Charles A. Micchelli

Opis

This volume contains articles that document the advances in the subject of Total Positivity during the last two decades. The material is divided into ten chapters. While some of the articles are of a survey nature, others present new results appearing here for the first time. Also, some papers contain introductory material and are therefore accessible to non-experts interested in becoming familiar with the important ideas and techniques of Total Positivity. Audience: This book will be of value to mathematicians, engineers and computer scientists whose work involves applications of Total Positivity to problems in the theory of spline functions, numerical quadrature, nonlinear analysis, entire functions, probability, mathematical biology, statistics, approximation theory, combinatorics, geometric modelling, matrix theory and integral equations.

Spis treści

Preface. I. Spline Functions. Total Positivity of the Spline Kernel and its Applications; B. Bojanov. Total Positivity Properties of LB-Splines; T. Lyche, L.L. Schumaker. Total Positivity and Splines; K. Mørken. Totally Positive Systems and Interpolation by Subspaces of Generalized Splines; M. Sommer. H. Strauss. II. Matrix Theory. Preservation of Total Nonnegativity under the Hadamard Product and Related Topics; J. Garloff, D.G. Wagner. Vertex Implications for Totally Nonnegative under the Hadamard Product and Related Topics; J. Garloff. On Factorizations of Totally Positive Matrices; J. Garloff. On Factorizations of Totally Positive Matrices; M. Gasca, J.M. Peña. III. Geometric Modeling. Total Positivity and Optimal Bases; J.M. Carnicer, J.M. Peña. Total Positivity and the Shape of Curves; T.N.T. Goodman. Tchebycheff Curves; M.L. Mazure, H. Pottmann. IV. Probability and Mathematical Biology. Analytical and Probabilistic Methods for Totally Positive Matrices; G.S. Goodman. Some Inequalities of Total Positivity in Pure and Applied Mathematics; S. Karlin, Z. Ziegler. New Directions and Problems of Multivariate Total Positivity Motivated by Genetic Recombination Probabilities; S. Karlin. V. Approximation Theory. Tchebycheff Spaces and Total Positivity; J.M. Carnicer, J.M. Peña. Cebysev and Weak Cebysev Systems; R.A. Zalik. VI. Complex Analysis. Zero Sets of Entire Fourier Transforms of Multiply Positive Density Functions; O.M. Katkova. VII. Statistics. Total Nonnegativity of Moment Matrices and its Application to E- Optimal Designs in Polynomial Regression; B. Heiligers. Analysis of Regression Dependence in 2 xn Bivariate Distributions and Some Applications in Contingency Tables; S. Kasala, M.B. Rao. VIII. Real Analysis. Total Positivity and Nonlinear Analysis; R.-Q. Jia. Solutions of Certain Functional Equations; S. Karlin. Alternance and Snakes in the Nonlinear Finite Moment Problem; K. Tatalian. IX. Combinatorics. The Applications of Total Positivity to Combinatorics, and Conversely; F. Brenti. X. Integral Equations. Spectral Properties of Totally Positive Kernels and Matrices; A. Pinkus. Index.