4 problems

Let a divergence-free three-dimensional vector wavelet basis consist of wavelet functions $\boldsymbol{\psi}_\lambda(\boldsymbol{x})$, and let $r$-regularity require rapid decrease…

Consider an orthonormal solenoidal wavelet basis on $\mathbb{R}^3$, obtained by the integral helical pull-up of a scalar basis. A wavelet is $r$-regular when it decreases rapidly a…

Let $\psi_\lambda$ be scalar wavelets used to construct an orthonormal solenoidal wavelet basis by helical pull-up, and let $r$-regularity mean rapid decrease of the wavelet functi…

Fix vectors $v_1,\dots,v_m\in\mathbb{R}^d$ with $1\le d\le m$. For integers $k$ satisfying $2\le k\le d$, let $|v_{i_1}\wedge\cdots\wedge v_{i_k}|$ denote the Euclidean norm of the…