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Positivity of One-Dimensional Operator 2mth Order on the Half-Line and its Applications

ABSTRACT In the present paper, the positivity of a multidimensional differential operator 2mth order in the half-space is established. The structure of fractional spaces generated by this operator is investigated. The equivalence of the norms of these fractional spaces in Hölder spaces is proved. The applications of the well posedness of boundary value problems for elliptic equations in a Hölder space is provided.