Chebyshev Splines and Kolmogorov Inequalities
Sergey Bagdasarov
Π΄Π΅ΠΊ. 2012β―Π³. Β· Operator Theory: Advances and Applications ΠΠ½ΠΈΠ³Π°Β 105 Β· BirkhΓ€user
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ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
210
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
reportΠΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΎΡΠ·ΡΠ²Ρ Π½Π΅ ΠΏΡΠΎΠ²Π΅ΡΠ΅Π½Ρ. ΠΠΎΠ΄ΡΠΎΠ±Π½Π΅Π΅β¦
ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations .
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Π§ΡΠΎΠ±Ρ ΠΎΡΠΊΡΡΡΡ ΠΊΠ½ΠΈΠ³Ρ Π½Π° ΡΠ°ΠΊΠΎΠΌ ΡΡΡΡΠΎΠΉΡΡΠ²Π΅ Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ, ΠΊΠ°ΠΊ Kobo, ΡΠΊΠ°ΡΠ°ΠΉΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄ΠΎΠ±Π°Π²ΡΡΠ΅ Π΅Π³ΠΎ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ. ΠΠΎΠ΄ΡΠΎΠ±Π½ΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΌΠΎΠΆΠ½ΠΎ Π½Π°ΠΉΡΠΈ Π² Π‘ΠΏΡΠ°Π²ΠΎΡΠ½ΠΎΠΌ ΡΠ΅Π½ΡΡΠ΅.
