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TUTCRIS

Quaternionic Hyperbolic Function Theory

Tutkimustuotosvertaisarvioitu

Yksityiskohdat

AlkuperäiskieliEnglanti
OtsikkoTopics in Clifford Analysis
KustantajaSpringer
Sivut25-52
Sivumäärä28
ISBN (elektroninen)978-3-030-23854-4
ISBN (painettu)978-3-030-23853-7
DOI - pysyväislinkit
TilaJulkaistu - 2019
OKM-julkaisutyyppiA3 Kirjan tai muun kokoomateoksen osa

Julkaisusarja

NimiTrends in Mathematics
ISSN (painettu)2297-0215
ISSN (elektroninen)2297-024X

Tiivistelmä

We are studying hyperbolic function theory in the skew-field of quaternions. This theory is connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric (Formula Presented) in the upper half space (Formula Presented). In the case k = 2, the metric is the hyperbolic metric of the Poincaré upper half-space. Hempfling and Leutwiler started to study this case and noticed that the quaternionic power function xm(m ε Z), is a conjugate gradient of a 2-hyperbolic harmonic function. They researched polynomial solutions. We find fundamental k-hyperbolic harmonic functions depending only on the hyperbolic distance and x3. Using these functions we are able to verify a Cauchy type integral formula. Earlier these results have been verified for quaternionic functions depending only on reduced variables (x0, x1, x2). Our functions are depending on four variables.

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