Edge-degenerate families of $\Psi$Do's on an infinite cylinder

TL;DR

This paper develops a parameter-dependent pseudo-differential calculus for an infinite cylinder, treating it as a manifold with conical exits to infinity, using edge-degenerate operators and operator-valued amplitudes.

Contribution

It introduces a new calculus for edge-degenerate pseudo-differential operators on infinite cylinders with parameter dependence.

Findings

Established a calculus for edge-degenerate pseudo-differential operators.

Formulated operators using operator-valued amplitude functions.

Applied the calculus to manifolds with conical exits to infinity.

Abstract

We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.