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. © 2010 IEEE.
|Original language||American English|
|State||Published - 29 Nov 2010|
|Event||Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings - |
Duration: 29 Nov 2010 → …
|Conference||Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings|
|Period||29/11/10 → …|
Campos, H. M., Perez, R. C., & Kravchenko, V. V. (2010). Construction and use of reproducing kernels for boundary and eigenvalue problems in the plane using pseudoanalytic function theory. Paper presented at Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings, . https://doi.org/10.1109/MMET.2010.5611413