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Information × Registration Number 0203U002511, 0100U005529 , R & D reports Title Methods of a harmonic analysis in a theory of functions and operators popup.stage_title Head Trigub R.M., Registration Date 10-04-2003 Organization Donetsk National University popup.description2 The positive definite finite radial functions of the polynomial kind and the maximal smoothness are constructed and their properties are investigated. The general direct theorem about approximation of functions on a segment of real axis by polynomials with hermitian interpolation in the given points and the account of position of the point is obtained. The theorem is complete and finishes longterm researches of mathematician from different centres of science. Theorems about unilateral and comonotone approaches of smooth function by polynomials with positive factors are proved. A specified combination of different restrictions on a function and polynomials, which approximates the function, is discussed. Certainly, in those cases when it is possible. Problems such as Pompeiu problems on manifolds are considered. The description of Pompeiu sets on a symmetric space in terms of approximation of their indicator functions is given. The canonical resolvents for dual pairs of operators are investigated. The formula such as Krein formula for resolvents is obtained. The theory of nonorthogonal operator measures in a hilbert space is studied. Absolutely continuous and singular spectra of the selfadjoint expansions of the symmetric operator in terms of their Weyl functions are described. Product Description popup.authors popup.nrat_date 2020-04-02 Close