Mathematical Sciences: Some Elementary Inequalities

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9401214 Bennett The project is concerned with the "little L-p" sequences spaces and their applications. Its main objective is to find new ways of making norm estimates for various classes of matrix transformations that are important in Analysis. Emphasis is on exact results, with best constants, and on "elementary inequalities," those involving matrices and sequences having non-negative entries. The theory of inequalities is crucial to the development of Modern Analysis. There are applications to probability theory, function theory, precision computations, stability of computation and order of growth. It is through inequalities that one has confidence in estimation and control of solutions to equations. ***