Notes on Fourier analysis (XLIV): On the summation of Fourier series
نویسندگان
چکیده
منابع مشابه
Notes on Fourier Series
A function or a real variable f is said to be periodic with period P if f(x+ P ) = f(x) holds for all x. Hence, if we know the values of f on an interval of length P , we know its values everywhere. If f is a function defined on an interval [a, b), we can extend f to a function defined for all x which is periodic of period b− a. We simply define f(x) to be f(x+ n(b− a)), where n is the integer ...
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A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...
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These are notes to accompany four lectures that I gave at the School on additive combinatorics, held in Montréal, Québec between March 30th and April 5th 2006. My aim is to introduce “quadratic fourier analysis” in so far as we understand it at the present time. Specifically, we will describe “quadratic objects” of various types and their relation to additive structures, particularly four-term ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1951
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245562