A Multivalued Logarithm on Time Scales
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.
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
Mathematics and Statistics
Keywords and Phrases
Cayley transformation; Cylinder transformation; Dynamic equations; Logarithm; Time scales
International Standard Serial Number (ISSN)
Article - Journal
© 2021 Elsevier, All rights reserved.
15 May 2021