Geodesic
Semigroups of operators and mixed properties of Banach space elements
Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 107-115

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With the aid of a finite collection of bounded strongly continuous semigroups of operators, we define mixed differences of elements, analogous to the mixed differences of functions of many variables defined over the whole space. The closure of the product of powers of generating operators is the analog of differentiation, generalized in the Sobolev sense. We establish relationships between the properties of differences of order $r+k$ and "$r$-differentiation". 
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     author = {A. P. Terekhin},
     title = {Semigroups of operators and mixed properties of {Banach} space elements},
     journal = {Matemati\v{c}eskie zametki},
     pages = {107--115},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a12/}
}
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A. P. Terekhin. Semigroups of operators and mixed properties of Banach space elements. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 107-115. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a12/