Integer functions, generalized functions, inequalities of Bernstain-Nikolsky, theorems of embedding, pseudodifferential operators are investigated in the paper aiming at the obtaining of exact acymptotical estimations for derivatives of integer functions, the construstion of the theory for spaces of Sobolev - Jurlich of an infinite order. The investigation of some actual and important problems of the theory of functions is also the aim of the paper. As a result the detailed investigation in the actual direction if the theory of functions has been held. New important results, having the complete character and containing solutions of some problems, have been obtained. New results in the theory of spaces of Sobolev and Sobolev - Jurlich of an infinite order, in the theory of pdeudodifferential operators have been obtained with the help of results and methods, developed in the paper. The paper results may find their field of application in mathematical analysis, differential equations and spaces of Sobolev of an infinite orderAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio
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