Nesterenko O. Inverse approximation problem and norms estimates for entire functions of exponential type and polynomials

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0407U000688

Thesis Registration Form

0407U000688.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

30-01-2007

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

The thesis is devoted to inverse approximation problems and to the establishment of certain estimates for the norms of entire functions and polynomials. The necessary and sufficient conditions are obtained for solvability of multiparameter inverse approximation problems by exponential type multivariable entire functions. Explicit formula for this solution is presented. A counterexample to show that second Jackson inequality with generalized Ditzian – Totik modulus of smoothness for comonotone approximation under some parameters isn’t true even with constant depending on a function is constructed. S.M.Nikolskii – type inequalities (inequalities involving different norms) for entire functions of exponential type, the improvement of some inequality for the norm of algebraic polynomials and its analogue for entire functions of exponential type are proved.

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Files

AVTOREF1.doc

Висновки--Висновки_дис.doc

Вступ--Вступ1.doc

Літерат--ЛІТЕР.doc

Розд1--Висновки1.doc

Розд1--пункт1.1.doc

Розд1--пункт1.2.doc

Розд1--пункт1.3.doc

Розд2--Висновки.doc

Розд2--пункт 2.4.doc

Розд2--пункт2.1.doc

Розд2--пункт2.2.doc

Розд2--пункт2.3.doc

Розд3--Висновки3.doc

Розд3--пункт3.1.doc

Розд3--пункт3.2.doc

Розд4--Висновки4.doc

Розд4--Розділ 2_1--Висновки.doc

Розд4--Розділ 2_1--пункт 2.5.doc

Розд4--Розділ 2_1--пункт2.1.doc

Розд4--Розділ 2_1--пункт2.2.doc

Розд4--Розділ 2_1--пункт2.3.doc

Розд4--Розділ 2_1--пункт2.4.doc

Розд4--пункт4.1.doc

Розд4--пункт4.2.doc

Розд4--пункт4.3.doc

Розд4--пункт4.4.doc

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