Functional Analysis

Download Modern Fourier Analysis: Preliminary Entry 250 (Graduate by Loukas Grafakos PDF

By Loukas Grafakos

the first aim of this article is to provide the theoretical beginning of the sphere of Fourier research. This publication is especially addressed to graduate scholars in arithmetic and is designed to serve for a three-course series at the topic. the one prerequisite for realizing the textual content is passable final touch of a path in degree concept, Lebesgue integration, and complicated variables. This e-book is meant to give the chosen subject matters in a few intensity and stimulate additional research. even though the emphasis falls on actual variable equipment in Euclidean areas, a bankruptcy is dedicated to the basics of study at the torus. This fabric is incorporated for historic purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic services in numerous variables.While the first version used to be released as a unmarried quantity, the hot version will include one hundred twenty pp of latest fabric, with an extra bankruptcy on time-frequency research and different glossy subject matters. consequently, the ebook is now being released in 2 separate volumes, the 1st quantity containing the classical subject matters (Lp areas, Littlewood-Paley conception, Smoothness, etc...), the second one quantity containing the fashionable themes (weighted inequalities, wavelets, atomic decomposition, etc...).From a overview of the 1st edition:“Grafakos’s booklet is particularly trouble-free with quite a few examples illustrating the definitions and ideas. it truly is more desirable for readers who are looking to get a think for present study. The therapy is carefully sleek with loose use of operators and sensible research. furthermore, not like many authors, Grafakos has in actual fact spent loads of time getting ready the exercises.” - Ken Ross, MAA Online

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