TY - JOUR
T1 - Dirichlet-Type Problems for the Two-Dimensional Helmholtz Operator in Complex Quaternionic Analysis
AU - Bory-Reyes, Juan
AU - Abreu-Blaya, Ricardo
AU - Hernández-Simon, Luis M.
AU - Schneider, Baruch
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - This study aims to study a class of Dirichlet-type problems associated with the two-dimensional Helmholtz equation with complex potential. Orthogonal decompositions of the complex quaternionic-valued Sobolev space as well as the corresponding orthoprojections onto the subspaces of theses decompositions are obtained. Analytic representation formulas for the underlying solutions in terms of hypercomplex integral operators are established.
AB - This study aims to study a class of Dirichlet-type problems associated with the two-dimensional Helmholtz equation with complex potential. Orthogonal decompositions of the complex quaternionic-valued Sobolev space as well as the corresponding orthoprojections onto the subspaces of theses decompositions are obtained. Analytic representation formulas for the underlying solutions in terms of hypercomplex integral operators are established.
KW - Dirichlet-type problems
KW - Helmholtz operator
KW - Quaternionic analysis
UR - http://www.scopus.com/inward/record.url?scp=84982300645&partnerID=8YFLogxK
U2 - 10.1007/s00009-016-0781-x
DO - 10.1007/s00009-016-0781-x
M3 - Artículo
SN - 1660-5446
VL - 13
SP - 4901
EP - 4916
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 6
ER -