Questions tagged [fa.functional-analysis]

Let $M$ be a compact connected smooth manifold. Write $C^{\infty}(M)$ for the Frechet space of the smooth real-valued functions on $M$ equipped with the usual $C^{\infty}$-topology. Given a compact ...

Let $\epsilon>0$ be small. Let $\eta(t) = \frac{2\epsilon}{\epsilon^2+(2\pi t)^2}$ (the Fourier transform of $x\mapsto e^{-\epsilon |x|}$). Let $V$ be the space of integrable, bounded functions $f:\...

This is a question of uncertainty-principle type stemming from Eigenvalue of a convolution and a restriction? Let $f:\mathbb{R}\to \mathbb{R}$ be even, absolutely continuous and supported in $[-\frac{...

I'm trying to estimate the fractal dimension of a function. I created the log(energies) Vs log(scales) plot and I'm computing the Fractal Dimension (D) from the slope using the relation $$ \alpha = -...

I came across this exercise and feel absolutely stuck: Let $p, q, r \in (1, \infty]$ be such that $1/p + 1/q = 1 + 1/r$. Suppose that $F : \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ satisfies ...

Let $M\in\mathbb{R}^{n\times n}$ be an invertible matrix, denote its induced linear map on $\mathbb{R}^n$ also by $M$, and let $f\in L^1(\mathbb{R}^n)$ be compactly supported. I am wondering if we can ...