Read e-book online Classical Fourier Analysis: Prelimianry Entry 249 (Graduate PDF

By Loukas Grafakos

the first objective of this article is to provide the theoretical beginning of the sector of Fourier research. This e-book is principally addressed to graduate scholars in arithmetic and is designed to serve for a three-course series at the topic. the one prerequisite for figuring out the textual content is passable finishing touch of a direction in degree concept, Lebesgue integration, and intricate variables. This publication is meant to give the chosen issues in a few intensity and stimulate extra learn. even if the emphasis falls on genuine variable equipment in Euclidean areas, a bankruptcy is dedicated to the basics of study at the torus. This fabric is incorporated for ancient purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic capabilities in numerous variables.While the first version used to be released as a unmarried quantity, the recent variation will comprise one hundred twenty pp of latest fabric, with an extra bankruptcy on time-frequency research and different glossy issues. therefore, the publication is now being released in 2 separate volumes, the 1st quantity containing the classical issues (Lp areas, Littlewood-Paley idea, Smoothness, etc...), the second one quantity containing the trendy subject matters (weighted inequalities, wavelets, atomic decomposition, etc...).From a evaluation of the 1st edition:“Grafakos’s publication is especially hassle-free with a number of examples illustrating the definitions and ideas. it truly is more advantageous for readers who are looking to get a suppose for present examine. The remedy is carefully sleek with loose use of operators and practical research. Morever, 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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Classical Fourier Analysis: Prelimianry Entry 249 (Graduate Texts in Mathematics) by Loukas Grafakos


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