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-$potentialThe 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. |

University of Bialystok |

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