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

By Loukas Grafakos

the first target of this article is to provide the theoretical beginning of the sector 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 single prerequisite for knowing the textual content is passable of completion of a path in degree idea, Lebesgue integration, and complicated variables. This e-book is meant to give the chosen subject matters in a few intensity and stimulate extra research. even though the emphasis falls on genuine variable equipment in Euclidean areas, a bankruptcy is dedicated to the basics of research at the torus. This fabric is integrated for ancient purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic features in numerous variables.While the first version was once released as a unmarried quantity, the hot version will comprise one hundred twenty pp of recent fabric, with an extra bankruptcy on time-frequency research and different glossy themes. consequently, the booklet 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 issues (weighted inequalities, wavelets, atomic decomposition, etc...).From a overview of the 1st edition:“Grafakos’s ebook is especially straight forward with a number of examples illustrating the definitions and ideas. it's improved for readers who are looking to get a consider for present learn. The therapy is punctiliously glossy with loose use of operators and sensible research. in addition, in contrast to many authors, Grafakos has truly spent loads of time getting ready the exercises.” - Ken Ross, MAA Online

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