# Pseudodifferential Operators on R^n with Variable Shifts

### Vladimir S. Rabinovich

Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico

## Abstract

The aim of the paper is the study of pseudodifferential operators with shifts of the form

where $a_j(x,D) \in OPS_{1,0}^m$ and $b_j(x,D) \in OPS_{1,0}^{m-\epsilon} \ \ (\epsilon > 0)$ are pseudodifferential operators in the H\"ormander classes, and $V_{h_j}$ and $T_{g_j}$ are shift operators of the form

where $h_j \in \mathbb R^n$ and the mappings $g_j: \, \mathbb R^n \to \mathbb R^n$ have infinitely differentiable coordinate functions bounded with all their derivatives. We will investigate the Fredholm and semi-Fredholm properties of the operator $A$ acting from $H^s(\mathbb R^n)$ into $H^{s-m}(\mathbb R^n)$ applying the limit operators method.

## Cite this article

Vladimir S. Rabinovich, Pseudodifferential Operators on R^n with Variable Shifts. Z. Anal. Anwend. 22 (2003), no. 2, pp. 315–338

DOI 10.4171/ZAA/1148