Structure of translation operators in the phase spaces of free Euclidean fields. I

V. I. Skripnik


Abstract: It is shown that in one class of Sovolev-type Hilbert spaces of functions on $\mathbf R^d$ the operator of translation along the coordinate axis $x^d$ has the semigroup property when projected onto the subspace of functions concentrated on the hypersurface $x^d=0$.

Received: 17.05.1977

 English version: Theoretical and Mathematical Physics, 1978, 35:1, 292–294

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