A Multivalued Logarithm on Time Scales

Author

Douglas R. Anderson
Martin Bohner, Missouri University of Science and TechnologyFollow

Abstract

A new definition of a multivalued 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 the wellspring 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.

Recommended Citation

D. R. Anderson and M. Bohner, "A Multivalued Logarithm on Time Scales," Applied Mathematics and Computation, vol. 397, Elsevier, May 2021.

The definitive version is available at https://doi.org/10.1016/j.amc.2021.125954

Department(s)

Mathematics and Statistics

Keywords and Phrases

Cayley transformation; Cylinder transformation; Dynamic equations; Logarithm; Time scales

International Standard Serial Number (ISSN)

0096-3003

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Elsevier, All rights reserved.

Publication Date

15 May 2021