Classical Fourier Analysis: Prelimianry Entry 249 (Graduate - download pdf or read online

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By Loukas Grafakos

the first aim of this article is to provide the theoretical starting place of the sphere of Fourier research. This e-book 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 provide the chosen subject matters in a few intensity and stimulate additional examine. even if the emphasis falls on actual variable tools in Euclidean areas, a bankruptcy is dedicated to the basics of research at the torus. This fabric is integrated for old purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic features in different variables.While the first version was once released as a unmarried quantity, the recent variation will include a hundred and twenty pp of latest fabric, with an extra bankruptcy on time-frequency research and different smooth subject matters. hence, the booklet is now being released in 2 separate volumes, the 1st quantity containing the classical themes (Lp areas, Littlewood-Paley thought, Smoothness, etc...), the second one quantity containing the trendy themes (weighted inequalities, wavelets, atomic decomposition, etc...).From a assessment of the 1st edition:“Grafakos’s e-book is particularly common with a variety of examples illustrating the definitions and concepts. it's greater for readers who are looking to get a suppose for present study. The therapy is carefully glossy with loose use of operators and useful research. Morever, in contrast to many authors, Grafakos has sincerely 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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