Kolmogorov problem in $W^rH^ω[0,1]$ and extremal Zolotarev ω-splines

Bagdasarov, Sergey K.

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Tytuł książki

Kolmogorov problem in $W^rH^ω[0,1]$ and extremal Zolotarev ω-splines

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Bagdasarov Sergey K.

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Rozprawy Matematyczne tom/nr w serii: 379 wydano: 1998

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CONTENTS
0. Introduction...........................................................................................5
1. Extrema of functionals in $H^ω[a,b]$ and perfect ω-splines................11
2. Auxiliary results...................................................................................22
3. Formulation of the main result.............................................................25
4. Proof of the main result.......................................................................32
5. The extrapolation problem...................................................................54
6. Maximization of functionals in $H^ω[a₁,a₂]$, -∞ ≤ a₁ < a₂ ≤ ∞..............56
7. Euler ω-splines on the finite interval....................................................62
Appendix A. Construction of Chebyshev splines.....................................68
Appendix B. Construction of Zolotarev splines........................................70
References.............................................................................................78

Słowa kluczowe

Chebyshev and Zolotarev polynomials perfect polynomial splines Sobolev classes $W^r_∞(I)$ Lipschitz and Hölder classes $W^rH^α(I)$ Weyl-Hölder-Nikol'skiĭ classes $W^rH^ω(I)$ Kolmogorov-Landau problem of sharp inequalities for intermediate derivatives modulus of continuity of a continuous function concave modulus of continuity ω Korneĭchuk Lemma on maximization of integral functionals with simple kernels Borsuk Antipodality Theorem perfect ω-splines extremal rearrangements numerical differentiation formulae Zolotarev, Chebyshev and Euler perfect ω-splines

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 379

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81

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Opis fizyczny

Dissertationes Mathematicae, Tom CCCLXXIX

Daty

wydano

1998

otrzymano

1997-06-02

poprawiono

1998-06-05

Twórcy

autor

Bagdasarov Sergey K.

skbgdsrv@math.ohio-state.edu

Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.

Bibliografia

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1991 Mathematics Subject Classification: Primary 41A17, 41A44; Secondary 26A15, 26A16, 26A51, 26D10, 46N10, 46N40, 47G10, 52A40, 58C30, 65D07, 65D25, 90C29, 90C26, 90C30.

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Książka - szczegóły

Kolmogorov problem in $W^rH^ω[0,1]$ and extremal Zolotarev ω-splines

Autorzy

Seria

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