Submission date: 3 January 2023

Abstract:

We show that unary log-analytic functions are polynomially bounded. In the higher dimensional case globally a log-analytic function can have exponential growth. We show that a log-analytic function is polynomially bounded on a definable set which contains the germ of every ray at infinity.

Mathematics Subject Classification: 03C64, 14P15, 26A09, 26A12, 32B20

Keywords and phrases:

Full text arXiv 2301.02187: pdf, ps.