6 problems

Let $p$ be a prime, let ${{\mathbb Q}}_p$ be the field of $p$-adic numbers, and let $\Omega(|x|_p)$ denote the characteristic function of the unit disc. A function $\phi$ satisfyin…

The preceding construction associates generalized filter systems to unitary-matrix-valued functions on ${\mathbb T}$ whose dimensions vary with $x\in{\mathbb T}$, and an analogue o…

A refinable distribution is a distribution satisfying the refinement equation associated with a dilation and translations; in this paper, scalar-valued means that the distribution…

Let $N$ be the dilation parameter, let ${\mathcal S}_N$ be the associated solenoid with measure $\tau$, and let the winding line be the image of the embedding of $\mathbb R$ into…

Benedetto–Benedetto conjecture. Other $p$-adic wavelets with the same set of translations cannot be constructed, and the corresponding MRA theory cannot be developed.

Let $p$ be a prime, let $I_p$ be the set of $p$-adic translation parameters used for shifts, and let $\phi$ be a compactly supported refinable function on $\mathbb{Q}_p$. Write…