### Abstract

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 |
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DOIs | |

State | Published - 29 Nov 2010 |

Event | Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings - Duration: 29 Nov 2010 → … |

### Conference

Conference | Mathematical Methods in Electromagnetic Theory, MMET, Conference Proceedings |
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Period | 29/11/10 → … |

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## Cite this

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