Some results for a class of generalized polynomials |
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Authors: | Morigi Serena Neamtu Marian |
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Institution: | (1) Department of Mathematics, University of Bologna, I‐40127 Bologna, Italy E-mail:;(2) Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA E-mail: |
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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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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