On extremal properties of Jacobian elliptic functions with complex modulus

Siegl, Petr; Štampach, František (2016). On extremal properties of Jacobian elliptic functions with complex modulus. Journal of mathematical analysis and applications, 442(2), pp. 627-641. Elsevier 10.1016/j.jmaa.2016.05.008

[img]
Preview
Text
1512.06089.pdf - Accepted Version
Available under License Publisher holds Copyright.

Download (616kB) | Preview
[img] Text
1-s2.0-S0022247X16301500-main.pdf - Published Version
Restricted to registered users only
Available under License Publisher holds Copyright.

Download (549kB) | Request a copy

A thorough analysis of values of the function m↦sn(K(m)u|m) for complex parameter m and u∈(0,1) is given. First, it is proved that the absolute value of this function never exceeds 1 if m does not belong to the region in C determined by inequalities |z−1|<1 and |z|>1. The global maximum of the function under investigation is shown to be always located in this region. More precisely, it is proved that if u≤1/2, then the global maximum is located at m=1 with the value equal to 1. While if u>1/2, then the global maximum is located in the interval (1,2) and its value exceeds 1. In addition, more subtle extremal properties are studied numerically. Finally, applications in a Laplace-type integral and spectral analysis of some complex Jacobi matrices are presented.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Siegl, Petr

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-247X

Publisher:

Elsevier

Funders:

[UNSPECIFIED] Swiss National Science Foundation

Projects:

Projects 0 not found.

Language:

English

Submitter:

Petr Siegl

Date Deposited:

11 Jul 2017 16:54

Last Modified:

16 Oct 2018 02:30

Publisher DOI:

10.1016/j.jmaa.2016.05.008

ArXiv ID:

1512.06089

BORIS DOI:

10.7892/boris.97805

URI:

https://boris.unibe.ch/id/eprint/97805

Actions (login required)

Edit item Edit item
Provide Feedback