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This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory.Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. ... Read more

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A collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. ... Read more

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A book dealing with several classes of Besov-Hardy-Sobolev function spaces on the Euclidean n-space and the n-torus. Periodic, weighted and anisotropic spaces are discussed, as well as spaces in which properties of dominating mixed smoothness predominate. In the first and last chapters, related spaces of entire analytic functions and abstract spaces are considered. The discussions in this book are based on the latest techniques of Fourier Analysis. ... Read more

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The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems.

One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the $(n-1)$-dimensional volume of hyperplane sections of the $n$-dimensional unit cube (it is $\sqrt{2}$ for each $n\geq 2$). Another is the Busemann-Petty problem: if $K$ and $L$ are two convex origin-symmetric $n$-dimensional bodies and the $(n-1)$-dimensional volume of each central hyperplane section of $K$ is less than the $(n-1)$-dimensional volume of the corresponding section of $L$, is it true that the $n$-dimensional volume of $K$ is less than the volume of $L$? (The answer is positive for $n\le 4$ and negative for $n>4$.)

The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis. ... Read more

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In a series of three papers published in 1930 and 1931, Paley and Zygmund44studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series. ... Read more

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Presents a new concept of modularization of pricing, with a new approach to searching systematically for new solutions in the Fourier space. Shows in detail the increased potential of this approach over the more volatile stochastic methods. Softcover. ... Read more

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In the theory of convergence and summability whether for ordinary Fourier series or other expansions emphasis is placed on the phenomenon of localization whenever such occurs, and in the present paper a certain aspect of this phenomenon will be studied for the problem of best approximation as well. ... Read more

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Dieses Lehrbuch hat sich zum Standardwerk in der Ausbildung von Ingenieuren, Naturwissenschaftlern und Informatikern entwickelt. Hervorgegangen aus langjähriger Lehrtätigkeit der Autoren an der Technischen Universität in München, bietet es Studenten technischer Disziplinen eine gründliche Einführung in alle relevanten Themen. Es stellt konkrete und studentenfreundliche Rechenschemata zur Verfügung, die hervorragend zur Prüfungsvorbereitung geeignet sind. Ideal geeignet als Vorlesungsbegleiter, Repetitorium für Prüfungen und Nachschlagewerk in der Praxis.

"... Eine charakteristische Besonderheit dieses Lehrbuches sind die zahlreichen und äußerst vielseitigen Anwendungsbeispiele aus Physik, Chemie, Biologie und vor allem der Mechanik und Elektrotechnik, mit denen die eingeführten Begriffe und hergeleiteten Formeln regelmäßig illustriert werden..." GAMM Mittgn.

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Fourier Analysis and Partial Differential Equations presents theproceedings of the conference held at Miraflores de la Sierra in June 1992.These conferences are held periodically to assess new developments and resultsin the field. The proceedings are divided into two parts. Four mini-coursespresent a rich and actual piece of mathematics assuming minimal background fromthe audience and reaching the frontiers of present-day research. Twenty lecturescover a wide range of data in the fields of Fourier analysis and PDE.This book, representing the fourth conference in the series, is dedicated to thelate mathematician Antoni Zygmund, who founded the Chicago School of FourierAnalysis, which had a notable influence in the development of the field andsignificantly contributed to the flourishing of Fourier analyis in Spain. ... Read more

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Activation Spectrometry in Chemical Analysis Susan J. Parry In clear, easy-to-read language, Activation Spectrometry in Chemical Analysis provides a straightforward review of just what activation analysis can do, describing the technique as it is currently applied to biomedical, environmental, geological, and industrial analytical problems. The book outlines the specifics of the procedures that have proven critical to the technique’s success and describes the current status of activation spectrometry in a concise, three-part format: principles, techniques, and applications. Written for undergraduates and postgraduates in universities, research institutes, government, or industry, the book provides the first definitive look at the day-to-day and key uses of the method that is at once challenging and intriguing, yet simple to grasp. 1991 (0 471-63844-7) 264 pp. Principles and Practice of Spectroscopic Calibration Howard Mark Clearly linking theory with applications, this unique guide to spectroscopic calibration advances an approach that is understandable, free of the usual uncertainties, and simple to execute. The book details the practical aspects of generating a calibration equation, as well as the basics of recognizing and dealing with different types of problems affecting calibration. Most of the procedures are applicable to such sophisticated and popular approaches as Principal Component Calibration (PCA), Partial Least Squares Calibration (PLS), and Fourier Transform Calibration. 1991 (0 471-54614-3) 192 pp. Analytical Raman Spectroscopy Edited by Jeanette G. Grasselli and Bernard J. Bulkin Analytical Raman Spectroscopy charts, through a series of contributed articles, the spectacular versatility of the method and its applications in semiconductor characterization, synthetic organic polymer analysis, organic and petrochemical analysis, heterogeneous catalysts, and biological studies. Chapters feature an outline structure which systematically details the critical aspects of each subject discussed. The book provides a unique look at the field’s fundamental operational techniques, instrumentation, and up-to-the-minute advances: components of modern Raman spectrometers; Raman spectroscopy of inorganic species in solution; quantitative analysis by Raman spectroscopy; and much more. 1991 (0 471-51955-3) 480 pp. ... Read more

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This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff.

The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space. ... Read more