New posts in Harmonic Analysis

Proving a sum of a strange series $ \sum_{i=1}^{n} 11i^{10}-55i^9+165i^8-330i^7+462i^6 -462i^5+330i^4-165i^3+55i^2-11i+1 = n^{11} $

When is convolution not commutative?

Is a homogeneous Banach space on $\mathbb T$ always well defined?

Solving the PDE $x_{1}\dfrac{\partial f}{\partial x_{1}}+x_{2}\dfrac{\partial f}{\partial x_{2}}=e^{f(x_{1},x_{2})}-\alpha.$

Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

Existence of a certain Schwartz function with compact Fourier support

Hölder norm of the Hilbert Transform

Fourier transform of the distribution PV $\left( \frac{1}{x} \right)$

Fourier transform of a complex exponential

A measure and the Fourier inverse transform of its Fourier transform