Pick Matricies and Quaternionic Power Series View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-10

AUTHORS

Vladimir Bolotnikov

ABSTRACT

It is well known that a non-constant complex-valued function f defined on the open unit disk D of the complex plane is an analytic self-mapping of D if and only if Pick matrices (1-f(zi)f(zj)¯)/(1-ziz¯j)i,j=1n are positive semidefinite for all choices of finitely many points zi∈D. A stronger version of the “if” part was established by Hindmarsh (Pac J Math 27:527–531, 1968): if all 3 × 3 Pick matrices are positive semidefinite, then f is an analytic self-mapping of D. In this paper, we extend this result to the non-commutative setting of power series over quaternions. More... »

PAGES

293-302

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-014-2173-6

DOI

http://dx.doi.org/10.1007/s00020-014-2173-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028062785


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