Chebyshevian splines

Zygmunt Wronicz

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1990

Abstract

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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....................................................................................................981985 Mathematics Subject Classification: 41A15, 46E15, 46B15

How to cite

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Zygmunt Wronicz. Chebyshevian splines. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268497>.

@book{ZygmuntWronicz1990,
abstract = {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....................................................................................................981985 Mathematics Subject Classification: 41A15, 46E15, 46B15},
author = {Zygmunt Wronicz},
keywords = {extended complete Chebyshev system; Canonical complete Chebyshev systems; Newton interpolation formula; Markov inequality; Chebyshevian splines; B-splines; Marsden identity; de Boor inequalities; orthogonal spline projections; modulus of smoothness},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Chebyshevian splines},
url = {http://eudml.org/doc/268497},
year = {1990},
}

TY - BOOK
AU - Zygmunt Wronicz
TI - Chebyshevian splines
PY - 1990
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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....................................................................................................981985 Mathematics Subject Classification: 41A15, 46E15, 46B15
LA - eng
KW - extended complete Chebyshev system; Canonical complete Chebyshev systems; Newton interpolation formula; Markov inequality; Chebyshevian splines; B-splines; Marsden identity; de Boor inequalities; orthogonal spline projections; modulus of smoothness
UR - http://eudml.org/doc/268497
ER -

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