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Classical and Multilinear Harmonic Analysis
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Classical and Multilinear Harmonic Analysis
"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary, and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form"--
Topics in Analysis and Its Applications
This book contains five theses in analysis, by A C Gilbert, N Saito, W Schlag, T Tao and C M Thiele. It covers a broad spectrum of modern harmonic analysis, from Littlewood–Paley theory (wavelets) to subtle interactions of geometry and Fourier oscillations. The common theme of the theses involves intricate local Fourier (or multiscale) decompositions of functions and operators to account for cumulative properties involving size or structure. Contents:Lp → Lq Estimates for the Circular Maximal Function (W Schlag)Three Regularity Results in Harmonic Analysis (T Tao)Time-Frequency Analysis in the Discrete Phase Plane (C M Thiele)Multiresolution Homogenization Schemes for Differential Equations and Applications (A C Gilbert)Local Feature Extraction and Its Applications Using a Library of Bases (N Saito) Readership: Researchers in the fields of analysis & differential equations, signal processing and applied mathematics. Keywords:Harmonic Analysis;Multilinear Singular Integrals;Walsh Functions;Convergence of Fourier Series;Fast Walsh Transform;Bilinear Hilbert Transform
Classical and Multilinear Harmonic Analysis
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Austrian Information
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You Can't Copy Tradition
The horrors of World War I left a mark on all of Europe as well as on the United States of America. Within the political, intellectual and academic life the catchphrase of international good will established itself. This term, rather this vision, must not be ignored in the context of the birth hour of the Austro-American Institute of Education, when international education was still in its infancy. The institute ́s founder, Paul Leo Dengler, seized an opportunity presented to him at the end of 1925 – apparently just in time amidst the pioneering spirit following World War I – to propose and present his Amerika-Institut in Vienna to leaders of the Institute of International Education in New York. Eventually, in March of 1926 the Austro-American Institute of Education (AAIE) was founded in Vienna. The idea of a comprehensive history of the AAIE is to shed light on the evolvement of some of the most significant intellectual forces that have been shaping international cultural relations over the past century. Volume I of AAIE ́s history takes a close look at the activities, programs, key-players and the bilateral mission of Dengler‘s institute during the years 1926 –1971.
Invariant Manifolds and Dispersive Hamiltonian Evolution Equations
The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface wh...
A Course in Complex Analysis and Riemann Surfaces
Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces...
A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations with Potentials
The authors study the Cauchy problem for the one-dimensional wave equation ∂2tu(t,x)−∂2xu(t,x)+V(x)u(t,x)=0. The potential V is assumed to be smooth with asymptotic behavior V(x)∼−14|x|−2 as |x|→∞. They derive dispersive estimates, energy estimates, and estimates involving the scaling vector field t∂t+x∂x, where the latter are obtained by employing a vector field method on the “distorted” Fourier side. In addition, they prove local energy decay estimates. Their results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space; see Donninger, Krieger, Szeftel, and Wong, “Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space”, preprint arXiv:1310.5606 (2013).
Analysis at Large
Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékop...
