Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second, we discuss the Hölder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra. Finally, we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
Nanbin CAO
,
Zunfeng LI
,
Heju YANG
,
Yuying QIAO
. CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS*[J]. Acta mathematica scientia, Series B, 2024
, 44(1)
: 369
-385
.
DOI: 10.1007/s10473-024-0120-4
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