XXIX Workshop on Geometric Methods in Physics 27.06-03.07.2010

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.

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