On extremal properties of Jacobian elliptic functions with complex modulus
Number of Authors: 2
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 442, no 2, 627-641 p.Article in journal (Refereed) Published
A thorough analysis of values of the function m bar right arrow sn(K(m)u vertical bar m) for complex parameter m and u is an element of (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 vertical bar z - 1 vertical bar <1 and vertical bar z vertical bar > 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.
Place, publisher, year, edition, pages
2016. Vol. 442, no 2, 627-641 p.
Jacobian elliptic functions, Complex modulus, Extrema of elliptic functions
IdentifiersURN: urn:nbn:se:su:diva-131900DOI: 10.1016/j.jmaa.2016.05.008ISI: 000377322700013OAI: oai:DiVA.org:su-131900DiVA: diva2:947231