Convergence of Fourier Series in L Space
نویسنده
چکیده
The convergence of Fourier series of trigonometric functions is easy to see, but the same question for general functions is not simple to answer. We study the convergence of Fourier series in Lp spaces. This result gives us a criterion that determines whether certain partial differential equations have solutions or not.We will follow closely the ideas from Schlag and Muscalu’s Classical and Multilinear Harmonic Analysis.
منابع مشابه
Harmonic Analysis: from Fourier to Haar Maŕıa
Contents Introduction xv Chapter 1. Fourier series: some motivation 1 1.1. Some examples and key definitions 1 1.2. Main questions 5 1.3. Fourier series and Fourier coefficients 7 1.4. A little history, and motivation from the physical world 11 Chapter 2. Interlude 17 2.1. Nested classes of functions on bounded intervals 17 2.2. Modes of convergence 28 2.3. Interchanging limit operations 34 2.4...
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