English

A Multi-Valued Logarithm on Time Scales

Classical Analysis and ODEs 2020-01-28 v1

Abstract

A new definition of a multi-valued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This new logarithm arises naturally from the definition of the cylinder transformation that is also at the heart of the definition of exponential functions on time scales. This definition will lead to a logarithm function on arbitrary time scales with familiar and useful properties that previous definitions in the literature lacked.

Keywords

Cite

@article{arxiv.2001.09347,
  title  = {A Multi-Valued Logarithm on Time Scales},
  author = {Douglas R. Anderson and Martin Bohner},
  journal= {arXiv preprint arXiv:2001.09347},
  year   = {2020}
}

Comments

Pre-print version 1, 17 pages

R2 v1 2026-06-23T13:20:39.054Z