CONTENTSIntroduction...........................................................................................................5I. Canonical complete Chebyshev systems 1. Canonical complete Chebyshev systems.......................................................7 2. Interpolation by generalized polynomials and divided differences................12 3. The Markov inequality for generalized polynomials......................................16II. Chebyshevian splines 1. Basic properties...........................................................................................18 2. B-splines......................................................................................................21 3. The Marsden identity...................................................................................28 4. De Boor's inequalities..................................................................................32 5. A recurrence relation for B-splines...............................................................37 6. Bounds on zeros..........................................................................................41III. Spline operators 1. Orthogonal spline projections .....................................................................46 2. Biorthogonal systems..................................................................................49 3. Equivalence of spline bases .......................................................................57 4. Positive spline operators and orthogonal splines .......................................60IV. Generalized moduli of smoothness and approximation by splines 1. Generalized moduli of smoothness .............................................................64 2. Generalization of the Whitney Theorem.......................................................70 3. Best approximation by splines......................................................................72 4. The Bernstein type inequality for splines ....................................................77V. Applications to approximation of analytic functions 1. Approximation by analytic splines................................................................78 2. Biorthogonal systems in the complex space A(D)........................................83 3. Systems conjugate to biorthogonal spline systems......................................86References.........................................................................................................94List of symbols....................................................................................................98
1985 Mathematics Subject Classification: 41A15, 46E15, 46B15
@book{bwmeta1.element.zamlynska-ec9d4745-4d5c-49ef-9b7b-f20a2b5e616c,
author = {Zygmunt Wronicz},
title = {Chebyshevian splines},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1990},
zbl = {0725.41010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-ec9d4745-4d5c-49ef-9b7b-f20a2b5e616c}
}
Zygmunt Wronicz. Chebyshevian splines. GDML_Books (1990), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-ec9d4745-4d5c-49ef-9b7b-f20a2b5e616c/