On eigenfunction expansions of piecewise smooth functions, associated with the power of the Schrödinger operator

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.

Keywords:

• eigenfunction expansions
• power of Schrödinger operator
• piecewise smooth functions

AMS Subject Classifications::

• Primary 42B08
• Secondary 42C14

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.