Kategoria BISAC: Mathematics >> Mathematical Analysis

Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since the first publication of this book, (Academic Press, 1985), the subject of positive operators and Riesz spaces has found many applications in several disciplines, including social sciences and engineering. It is well known that many linear operators between Banach spaces arising in classical analysis are in fact positive operators. Therefore we study here positive operators in the setting of Riesz spaces and Banach lattices and from both the...

This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation,...

Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation....

Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate and multivariate cases. Next the right and left, as well as mixed, Landau fractional differentiation inequalities in the univariate and multivariate cases are illustrated. Throughout the book many applications are given....

This volume assesses the difficulties involved in real-time communication via a single-input/single-output system with complex random variables. As a result, the most important aspects of a SAEC are presented, including the identification of the echo paths with adaptive filters, double-talk detection, and suppression.

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely...

This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a...

This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems and displays how variousapproachescan easily beappliedto a range of model cases.

Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is apractical text for an introductory course or seminar on nonlinear functional analysis."

This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.This global point of view is takenby focussing on the issues involved in determining the appropriate...

The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the...

This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in...