TY - GEN
T1 - Construction and use of reproducing kernels for boundary and eigenvalue problems in the plane using pseudoanalytic function theory
AU - Campos, Hugo M.
AU - Perez, Raul Castillo
AU - Kravchenko, Vladislav V.
PY - 2010
Y1 - 2010
N2 - We show how the Bergman-type reproducing kernels for the elliptic operator D= div p grad + q with variable coefficients defined in a bounded domain in the plane can be constructed using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q and with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be obtained following a simple algorithm consisting in recursive integration. Then the complete system of solutions is used for constructing the corresponding reproducing kernel. We study theoretical and numerical aspects of the method.
AB - We show how the Bergman-type reproducing kernels for the elliptic operator D= div p grad + q with variable coefficients defined in a bounded domain in the plane can be constructed using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q and with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be obtained following a simple algorithm consisting in recursive integration. Then the complete system of solutions is used for constructing the corresponding reproducing kernel. We study theoretical and numerical aspects of the method.
UR - http://www.scopus.com/inward/record.url?scp=78649255845&partnerID=8YFLogxK
U2 - 10.1109/MMET.2010.5611413
DO - 10.1109/MMET.2010.5611413
M3 - Contribución a la conferencia
AN - SCOPUS:78649255845
SN - 9781424488612
T3 - Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings
BT - 2010 International Conference on Mathematical Methods in Electromagnetic Theory, MMET-10 - Conference Proceedings
T2 - 2010 International Conference on Mathematical Methods in Electromagnetic Theory, MMET-10
Y2 - 6 September 2010 through 8 September 2010
ER -