A multivalued logarithm on time scales

被引：6

作者：

Anderson, Douglas R. ^{[1
]}

Bohner, Martin ^{[2
]}

机构：

[1] Concordia Coll Moorhead, Dept Math, Moorhead, MN 56562 USA

[2] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 397卷

关键词：

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

D O I：

10.1016/j.amc.2021.125954

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：13

共 12 条

[1]

Anderson D. R., 2020, Conformable Dynamic Equations on Time Scales

[2]

[Anonymous], 2018, FRACTIONAL DYNAMIC C

[3] The logarithm on time scales [J].

Bohner, M .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2005, 11 (15) :1305-1306

[4]

Bohner M., 2016, Multivariable Dynamic Calculus on Time Scales

[5]

Bohner M., 2003, ADV DYNAMIC EQUATION, DOI DOI 10.1007/978-0-8176-8230-9

[6] New definitions of exponential, hyperbolic and trigonometric functions on time scales [J].

Cieslinski, Jan L. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (01) :8-22

[7] A dynamic matrix exponential via a matrix cylinder transformation [J].

Cuchta, Tom ;

Grow, David ;

Wintz, Nick .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) :733-751

[8]

Hilger S., 1990, Results. Math, V18, P18, DOI [10.1007/BF03323153, DOI 10.1007/BF03323153]

[9]

Huff S, 2003, DISCRETE CONT DYN-A, P423

[10] APPLICATIONS OF ITERATED LOGARITHM FUNCTIONS ON TIME SCALES TO RIEMANN-WEBER-TYPE EQUATIONS [J].

Ito, Baku ;

Rehak, Pavel ;

Yamaoka, Naoto .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (04) :1611-1624

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