Structure of translation operators in the phase spaces of free Euclidean fields.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 24-28

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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 $x^d=0$.
@article{TMF_1978_35_1_a2,
     author = {V. I. Skripnik},
     title = {Structure of translation operators in the phase spaces of free {Euclidean} {fields.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a2/}
}
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V. I. Skripnik. Structure of translation operators in the phase spaces of free Euclidean fields.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 1, pp. 24-28. http://geodesic.mathdoc.fr/item/TMF_1978_35_1_a2/