The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423036" target="_blank" >RIV/00216208:11320/20:10423036 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6zYxXcsT05" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6zYxXcsT05</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40315-020-00322-z" target="_blank" >10.1007/s40315-020-00322-z</a>
Alternative languages
Result language
angličtina
Original language name
The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis
Original language description
As is the case for the theory of holomorphic functions in the complex plane, the Cauchy Integral Formula has proven to be a cornerstone of Clifford analysis, the monogenic function theory in higher dimensional euclidean space. In recent years, several new branches of Clifford analysis have emerged. Similarly as to how hermitian Clifford analysis in euclidean space R^2n of even dimension emerged as a refinement of euclidean Clifford analysis by introducing a complex structure on R^2n, quaternionic Clifford analysis arose as a further refinement by introducing a so-called hypercomplex structure Q, i.e. three complex structures (I, J, K) which follow the quaternionic multiplication rules, on R^4p, the dimension now being a fourfold. Two, respectively four, differential operators lead to first order systems invariant under the action of the respective symmetry groups U(n) and Sp(p). Their simultaneous null solutions are called hermitianmonogenic and quaternionicmonogenic functions respectively. In this contribution we further elaborate on the Cauchy Integral Formula for hermitian and quaternionic monogenic functions. Moreover we establish Caychy integral formulae for osp(4|2)-monogenic functions, the newest branch of Clifford analysis refining quaternionic monogenicity by taking the underlying symplectic symmetry fully into account.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-11473S" target="_blank" >GA20-11473S: Symmetry and invariance in analysis, geometric modelling and control theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computational Methods and Function Theory
ISSN
1617-9447
e-ISSN
—
Volume of the periodical
20
Issue of the periodical within the volume
3-4
Country of publishing house
DE - GERMANY
Number of pages
34
Pages from-to
431-464
UT code for WoS article
000542081500001
EID of the result in the Scopus database
2-s2.0-85086777972