Malaysian Journal of Mathematical Sciences, April 2017, Vol. 11(S)
Special Issue: The 2nd International Conference and Workshop on Mathematical Analysis (ICWOMA 2016)
The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in \(L_p\) Classes
Jamaludin, N. A. and Ahmedov, A.
Corresponding Email: amalinajamaludin@upnm.edu.my
Received date: -
Accepted date: -
Abstract:
In this paper the eigenfunction expansions of the Schrödinger operator with the potential having singularity at one point are considered. The uniform estimations for the spectral function of the Schrödinger operator in closed domain are obtained. The almost everywhere convergence of the eigenfunction expansions by Riesz means in the classes \(L_p\) classes is proven by estimating the maximal operator in \(L_1\) and \(L_2\) and applying the interpolation theorem for the family of linear operators.
Keywords: Schrödinger operator, almost everywhere convergence and eigenfunction expansions
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