A Multivalued Logarithm on Time Scales

Douglas R. Anderson; Martin Bohner

doi:10.1016/j.amc.2021.125954

A Multivalued Logarithm on Time Scales

Douglas R. Anderson
, Martin Bohner

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Applied Mathematics and Computation
Volume	397
DOIs	https://doi.org/10.1016/j.amc.2021.125954
State	Published - May 15 2021

Keywords

Cayley transformation
Cylinder transformation
Dynamic equations
Logarithm
Time scales

Disciplines

Mathematics
Statistics and Probability

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10.1016/j.amc.2021.125954License: Unspecified

https://doi.org/10.1016/j.amc.2021.125954

Cite this

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title = "A Multivalued Logarithm on Time Scales",

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 = "Cayley transformation, Cylinder transformation, Dynamic equations, Logarithm, Time scales",

author = "Anderson, \{Douglas R.\} and Martin Bohner",

year = "2021",

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AU - Bohner, Martin

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N2 - 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.

AB - 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.

KW - Cayley transformation

KW - Cylinder transformation

KW - Dynamic equations

KW - Logarithm

KW - Time scales

UR - https://scholarsmine.mst.edu/math_stat_facwork/1045

UR - https://doi.org/10.1016/j.amc.2021.125954

U2 - 10.1016/j.amc.2021.125954

DO - 10.1016/j.amc.2021.125954

M3 - Article

VL - 397

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

A Multivalued Logarithm on Time Scales

Abstract

Keywords

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