Quasianalytic ultradifferentiability cannot be tested in lower dimensions

TL;DR

This paper demonstrates that, unlike real analytic functions, quasianalytic ultradifferentiability cannot be verified by examining lower-dimensional slices, highlighting a fundamental difference in their structural properties.

Contribution

It proves that quasianalytic ultradifferentiability cannot be tested in lower dimensions, contrasting with the real analytic case, using a construction by Jaffe.

Findings

Quasianalytic ultradifferentiability cannot be tested in lower dimensions.

Contrasts with the real analytic case.

Uses a construction due to Jaffe.

Abstract

We show that, in contrast to the real analytic case, quasianalytic ultradifferentiability can never be tested in lower dimensions. Our results are based on a construction due to Jaffe.