Related papers: $p$-Adic multidimensional wavelets and their appli…

In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space,…

We introduce $p$-adic operator algebras, which are nonarchimedean analogues of $C^*$-algebras. We demonstrate that various classical examples of operator algebras - such as group(oid) $C^*$-algebras - have nonarchimedean counterparts. The…

Wan proved the rationality of partial toric $L$-functions using $\ell$-adic techniques. In this paper, we present a $p$-adic proof in the spirit of Dwork. We demonstrate that partial $L$-functions can be expressed as an alternating product…

In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…

On the space $\mathbb Q_p^n$, where $p\ne 2$ and $p$ does not divide $n$, we construct a p-adic counterpart of spherical coordinates. As applications, a description of homogeneous distributions on $\mathbb Q_p^n$ and a skew product…

We construct Fourier transforms relating functions and distributions on finite height $p$-divisible rigid analytic groups and objects in a dual category of $\mathbb{Z}_p$-local systems with analyticity conditions. Our Fourier transforms are…

This dissertation concerns the pseudo-differential operators of type 1,1. These have been known especially since around 1980, when it was shown that they play an important role in the treatment of fully non-linear partial differential…

Following Schweiger's generalization of multidimensional continued fraction algorithms, we consider a very large family of $p$-adic multidimensional continued fraction algorithms, which include Schneider's algorithm, Ruban's algorithms, and…

In this article, we present a new linear independence criterion for values of the $p$-adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear independence of some families of values of the $p$-adic Hurwitz…

The purpose of this note is to show how some results from the theory of partial differential equations apply to the study of pseudo-spectra of non-self-adjoint operators, which is a topic of current interest in applied mathematics.

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does…

We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on…

We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent…

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of…

In this paper we continue with the program to explore the topography of the space of W-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko and Roger on the algebra of q-deformed pseudodifferential…

We use radial estimates for pseudodifferential operators to describe long time evolution of solutions to $ i u_t - P u = f $ where $ P $ is a self-adjoint 0th order pseudodifferential operator satisfying hyperbolic dynamical assumptions and…

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic $\Psi$DO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [PST03] to a…

The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general…

We develop a framework for Poisson geometry on loop spaces of low regularity, extending Mokhov's classical constructions from smooth loops to weak Sobolev spaces $W^{s,p}(\mathbb{S^1},\mathbb{R}^m)$ with $o < s \frac{1}{2}$ and $1 < p <…