Newbetuts

Solving Poisson's equation for $\varrho(\mathbf{r}) = \sigma \cos\left(\frac{2 \pi}{L} x\right) \, \delta(y)$

Why is $\hat f(\xi)/\xi\in L^1(\mathbb R)$ when $f\in L^1$ is odd,$\hat f'(0)$ exists, and $\hat f(\xi)$ always has the same sign as $\xi$?

Another integral with Catalan

Which function's Fourier transform is the function itself?

Zeros of Fourier transform of a function in $C[-1,1]$

Is there a way to relate prime numbers and the Fourier transform?

Hardy–Littlewood-Sobolev inequality without Marcinkiewicz interpolation?

How do I compute the eigenfunctions of the Fourier Transform?

What's the connection between the Laplace transform and the Fourier transform?

Proving that : $ \left|\int_a^b\frac{\widehat{f}(\xi)}{\xi}d\xi\right|\le 4 \|f\|_1$ for all $a,b$ and all $f$

An apparent counterexample of the derivative proprety of Fourier transform

Differential operator applied to convolution

Decaying Fourier transform and smoothness

Dirichlet problem on $[0,1] \times [0, \pi]$

Fourier transform of $f(x)=\frac{1}{e^x+e^{-x}+2}$

New posts in fourier-analysis

Lower Bound on Oscillatory Integral

Decay of Fourier Coefficients and Smoothness

Slowest decay for Fourier transform of test functions.

On Vanishing Riemann Sums and Odd Functions

Isoperimetric inequality implies Wirtinger's inequality

Solving Poisson's equation for $\varrho(\mathbf{r}) = \sigma \cos\left(\frac{2 \pi}{L} x\right) \, \delta(y)$

Why is $\hat f(\xi)/\xi\in L^1(\mathbb R)$ when $f\in L^1$ is odd,$\hat f'(0)$ exists, and $\hat f(\xi)$ always has the same sign as $\xi$?

Another integral with Catalan

Which function's Fourier transform is the function itself?

Zeros of Fourier transform of a function in $C[-1,1]$

Is there a way to relate prime numbers and the Fourier transform?

Hardy–Littlewood-Sobolev inequality without Marcinkiewicz interpolation?

How do I compute the eigenfunctions of the Fourier Transform?

What's the connection between the Laplace transform and the Fourier transform?

Proving that : $ \left|\int_a^b\frac{\widehat{f}(\xi)}{\xi}d\xi\right|\le 4 \|f\|_1$ for all $a,b$ and all $f$

An apparent counterexample of the derivative proprety of Fourier transform

Differential operator applied to convolution

Decaying Fourier transform and smoothness

Dirichlet problem on $[0,1] \times [0, \pi]$

Fourier transform of $f(x)=\frac{1}{e^x+e^{-x}+2}$