Abstract
The eigenfunction expansions of an integer power of the Schrödinger operator in an arbitrary two-dimensional domain are considered. The convergence of the corresponding expansions of piecewise smooth functions is proved. When the dimension of the domain is greater than two, then it is well known that this result is not valid any more.
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Acknowledgements
This work was done during the first author's visit to the Institute of Advanced Technology (ITMA), University of Putra Malaysia. R. Asharov gratefully acknowledges ITMA for support and hospitality. S. Karaev wishes to express his deep gratitude to ICTP, Trieste, Italy for support.