List questions from fourier-analysis

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Dirichlet conditions for the existence of the Fourier transform

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Fourier Analysis an Introduction chap3 Problem 2

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If $f \in L^{1}(\mathbb{T})$ and $\sum_{n \in \mathbb{Z}} |{\hat{f}(n)}| < \infty $ then $f \in C^{0}(\mathbb{T})$

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Series expansion of $\ln(1+\exp(ix))$

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rudin math analysis - fourier seris, why fourier series is real if and only $c_{-n}=\overline{c_{n}}$

Published on 13 Apr 2019 - 2:25

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2D Fourier Transform of the PDE $u_{xx}+u_{tt}=g(x,t)$

Published on 13 Apr 2019 - 4:22

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Differentiability of the function defined by $\sum_{n\geq 1 } \sin n^2 x / n^{5/2} $

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Evaluate using convolution theorem $\int_0^\infty \frac{1}{(a^2+t^2)(b^2+t^2)} dt$

Published on 13 Apr 2019 - 7:42

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Solving the PDE $ku_{xx}(x,t)=u_t(x,t)$ Using Fourier Transforms

Published on 14 Apr 2019 - 0:58

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Asymptotic behavior of $f(x) = \sum_{n\geq 1 } a_n \cos n x $

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Proving $\int_{0}^{\infty}\frac{w^3\sin(wx)}{w^4+4} \ dw=\frac{\pi}{2}e^{-x}\cos(x)$

Published on 14 Apr 2019 - 7:33

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Fejer kernel, an alternative definition on (0,1)

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Convolution example

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Proof in Variational Gaussian Approximation

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List Question

Find function $f$ such that $(p*f)(x) = xf(x)$

Dirichlet conditions for the existence of the Fourier transform

Fourier Analysis an Introduction chap3 Problem 2

If $f \in L^{1}(\mathbb{T})$ and $\sum_{n \in \mathbb{Z}} |{\hat{f}(n)}| < \infty $ then $f \in C^{0}(\mathbb{T})$

Series expansion of $\ln(1+\exp(ix))$

rudin math analysis - fourier seris, why fourier series is real if and only $c_{-n}=\overline{c_{n}}$

2D Fourier Transform of the PDE $u_{xx}+u_{tt}=g(x,t)$

Differentiability of the function defined by $\sum_{n\geq 1 } \sin n^2 x / n^{5/2} $

Evaluate using convolution theorem $\int_0^\infty \frac{1}{(a^2+t^2)(b^2+t^2)} dt$

Solving the PDE $ku_{xx}(x,t)=u_t(x,t)$ Using Fourier Transforms

Asymptotic behavior of $f(x) = \sum_{n\geq 1 } a_n \cos n x $

Proving $\int_{0}^{\infty}\frac{w^3\sin(wx)}{w^4+4} \ dw=\frac{\pi}{2}e^{-x}\cos(x)$

Fejer kernel, an alternative definition on (0,1)

Convolution example

Proof in Variational Gaussian Approximation

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