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Chebyshevian splines

100%

Wronicz Z.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction...........................................................................................................5 I. 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......................................16 II. 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..........................................................................................41 III. Spline operators 1. Orthogonal spline projections .....................................................................46 2. Biorthogonal systems..................................................................................49 3. Equivalence of spline bases .......................................................................57 4. Positive spline operators and orthogonal splines .......................................60 IV. 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 ....................................................77 V. 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......................................86 References.........................................................................................................94 List of symbols....................................................................................................98

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On approximation by Chebyshevian box splines

96%

Wronicz Z.

Annales Polonici Mathematici

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2002

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tom 78

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nr 2

111-121

EN

Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions $w_{j}$ are of the form $w_{j}(x) = W_{j}(v_{n+j}·x)$, where the functions $W_{j}$ are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.

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On some generalization of box splines

96%

Wronicz Z.

Annales Polonici Mathematici

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1999

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tom 72

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nr 3

261-271

EN

We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.

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On some properties of LB-splines

37%

Wronicz Z.

Annales Polonici Mathematici

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1985

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tom 46

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nr 1

379-388

Ograniczanie wyników

3 Annales Polonici Mathematici

4 Wronicz Z.

1 2002

1 1999

1 1990

1 1985

Chebyshevian splines

On approximation by Chebyshevian box splines

On some generalization of box splines

On some properties of LB-splines