A class of generalized polynomials is considered consisting of the null spaces of certain differential operators with constant coefficients. This class strictly contains ordinary polynomials and appropriately scaled trigonometric polynomials. An analog of the classical Bernstein operator is introduced and it is shown that generalized Bernstein polynomials of a continuous function converge to this function. A convergence result is also proved for degree elevation of the generalized polynomials. Moreover, the geometric nature of these functions is discussed and a connection with certain rational parametric curves is established. © J.C. Baltzer AG, Science Publishers.

Some results for a class of generalized polynomials / Morigi S.; Neamtu M.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 12:2-3(2000), pp. 133-149.

Some results for a class of generalized polynomials

Morigi S.;
2000

Abstract

A class of generalized polynomials is considered consisting of the null spaces of certain differential operators with constant coefficients. This class strictly contains ordinary polynomials and appropriately scaled trigonometric polynomials. An analog of the classical Bernstein operator is introduced and it is shown that generalized Bernstein polynomials of a continuous function converge to this function. A convergence result is also proved for degree elevation of the generalized polynomials. Moreover, the geometric nature of these functions is discussed and a connection with certain rational parametric curves is established. © J.C. Baltzer AG, Science Publishers.
2000
Some results for a class of generalized polynomials / Morigi S.; Neamtu M.. - In: ADVANCES IN COMPUTATIONAL MATHEMATICS. - ISSN 1019-7168. - STAMPA. - 12:2-3(2000), pp. 133-149.
Morigi S.; Neamtu M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/879663
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