Offers a treatment of Fourier Series, Fourier Transforms, and FFTs. This title covers topics such as applications to vibrating strings, heat conduction, removal of noise and frequency detection, and filtering of Fourier Series and improvement of convergence.

This text on functional analysis in applied mathematics and engineering introduces basic function spaces and operators early so that the student can study problems at great length in the Hilbert space setting. A firm foundation for the subject is established by covering the spectral theorem for unbounded operators and the abstract evolution semi-group theory for time-dependent linear partial differential equations. Over 200 exercises are included in the text and a solutions manual is available for the instructor. The book should be useful to control engineers from the disciplines of...

Inflammatory Cells and Mediators in Bronchial Asthma provides reviews and summaries regarding state-of-the-art articles that examine the role of various inflammatory cells and their mediators in the pathogenesis of asthma. Topics include pharmacological and biochemical regulation of the airways; involvement of key inflammatory cells and the release and effect of their mediators in airway function; and the characteristics of receptors for leukotriene B4, C4, and D4, adenosine, platelet-activating factor, sensory and inflammatory peptides, and the effect of various anti-asthmatic drugs on...

An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented.
The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and...

Offers an introduction to the basic properties of wavelets, from background math to powerful applications. This book provides elementary methods for constructing wavelets, and illustrates several classes of wavelets. It offers a description of local sine and cosine bases that have been shown to be very effective in applications.

This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and pi: Z (r) Y is a Riemannian submersion.
After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure...

This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis.
All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex...

The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces.
Nine chapters introduce the main...

Several distinctive aspects make Dynamical Systems unique, including:
treating the subject from a mathematical perspective with the proofs of most of the results included
providing a careful review of background materials
introducing ideas through examples and at a level accessible to a beginning graduate student
focusing on multidimensional systems of real variables
The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but...