TY - JOUR
T1 - Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane
AU - Campos, Hugo M.
AU - Castillo-Pérez, Raúl
AU - Kravchenko, Vladislav V.
N1 - Funding Information:
This research was supported by CONACYT, Mexico via the research project 50424. H.M. Campos acknowledges the support by FCT, Portugal and CONACYT. R. Castillo-Pérez wishes to thank the support from CONACYT and National Polytechnic Institute for the possibility of a postdoctoral stay in the Department of Mathematics of the CINVESTAV in Queretaro, as well as from the SIBE and EDI programs and project 20113647 of the National Polytechnic Institute, Mexico.
PY - 2012/7
Y1 - 2012/7
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 and apply it to solve boundary value and eigenvalue problems for the stationary Schrödinger operator in bounded domains.
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 and apply it to solve boundary value and eigenvalue problems for the stationary Schrödinger operator in bounded domains.
KW - Bergman kernel
KW - Schrödinger equation
KW - generalized analytic function
KW - pseudoanalytic function
KW - reproducing kernel
UR - http://www.scopus.com/inward/record.url?scp=84863941932&partnerID=8YFLogxK
U2 - 10.1080/17476933.2011.611941
DO - 10.1080/17476933.2011.611941
M3 - Artículo
SN - 1747-6933
VL - 57
SP - 787
EP - 824
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 7-8
ER -