A multivalued logarithm on time scales

Douglas R. Anderson and Martin Bohner

Applied Mathematics and Computation, 2021, vol. 397, issue C

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.

Keywords: Dynamic equations; Cylinder transformation; Logarithm; Time scales; Cayley transformation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300321000023

DOI: 10.1016/j.amc.2021.125954

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