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Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures are functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. This book can serve as a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes several new results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and contains a number of exercises with hints to solutions as well as several open problems with suggestions for further research.
Functional analysis. --- Mathematics. --- Measure theory. --- Measure theory --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Applied Physics --- Uniform spaces. --- Measurement. --- Measuring --- Mensuration --- Spaces, Uniform --- Structures, Uniform --- Uniform structures --- Fourier analysis. --- Functions of complex variables. --- Functional Analysis. --- Fourier Analysis. --- Functions of a Complex Variable. --- Technology --- Metrology --- Physical measurements --- Quasi-uniform spaces --- Topology --- Nearness spaces --- Complex variables --- Elliptic functions --- Functions of real variables --- Analysis, Fourier --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic and hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by equations describing the evolution in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among the major sources of motivation and applications of new developments in nonlinear analysis and other mathematical theories. The theory of infinite dimensional dynamical systems has also increasingly important applications in the physical, chemical and life sciences. This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of 2008. As the conference was dedicated to Professor George Sell from University of Minnesota on the occasion of his 70th birthday, this collection reflects his pioneering work and influence in core areas of dynamical systems, including non-autonomous dynamical systems, skew-product flows, invariant manifolds theory, infinite dimensional dynamical systems, approximation dynamics, and fluid flows.
Differentiable dynamical systems. --- Differential equations -- Congresses. --- Stochastic differential equations. --- Differentiable dynamical systems --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Geometry --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations, partial. --- Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations --- 517.91 Differential equations --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Differential equations. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics
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