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Information × Registration Number 0307U009138, 0106U001947 , R & D reports Title The analysis of Fourier, the equation of convolution, approximation of functions popup.stage_title Наближення функцій поліномами з обмеженнями. Теореми єдиності для функцій із заданими інтегральними середніми. Head Trigub Roald Mikhailovich, Registration Date 24-12-2007 Organization Donetsk National University popup.description2 New inequalities for comparison of linear differential operators with constant coeffitients in spaces C and L_p are obtained at different p> =1 from functions from classes W^r on a circle, a straight line and a ray. With the help of positive definite functions the known inequality for series of Mathieu is proved. At all admissible values of parameters the principal term in an asymptotics for series of Mathieu is found. Analogs of the known theorem of L.Schwarz’s about the spectral analysis in R for set of equationses of convolution invariant concerning unitary transformations and the deformed shifts are considered. Similar problems are investigated for set of equationses of convolution on the reduced group of Heisenberg. One of outcomes of these researches is the refutation of a known hypothesis of S.Sangavelu about structure of invariant subspaces concerning the indicated transformations to space of continuous functions on a complex Euclidean space. Product Description popup.authors popup.nrat_date 2020-04-02 Close