XXIX Workshop on Geometric Methods in Physics 27.06-03.07.2010
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# Anatolij Antonevich

## On high order partial differential expressions with $\delta-$potential

The talk is devoted to the study of the
formal differential expressions
$$(-\Delta)^l u + a \delta u$$ for arbitrary $l$ and arbitrary
dimension of the space $\mathbb{R}^d$. Approximations of the
singular part by means of a family of rank-one operators are
constructed and
resolvent convergence of this family is investigated.
It is demonstrated, that the construction of self-adjoint operators in the space $L^2( R^d),$ corresponding to this expression, is connected with the
problem of multiplication of distributions.