3.2 Representation forms for a trigonometric polynomial
Let us consider the 2[pi]-periodic trigonometric polynomial
operator (or summability operator)
Teslic, "Comparative analysis of error distribution for symmetric hysteresis loop curves approximation by means of cosine and trigonometric polynomial
", presented at the 2nd Int.
For instance, Han presented the quadratic  and cubic  trigonometric polynomial
curves with a shape parameter.
Since the smooth periodic function Fp can be approximated well by the partial sum of its Fourier series [5,7,10], from this inequality, we see that we have constructed a trigonometric polynomial
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which can approximate to f on [OMEGA] very well.
Han, "Piecewise quadratic trigonometric polynomial
curves," Mathematics of Computation, vol.
The subdivision scheme is called vector subdivision scheme if the corresponding subdivision symbol is a matrix of trigonometric polynomial
. Note that the vector subdivision scheme plays an important role in multiwavelet and multichannel wavelets analysis; see [3-5] and references therein.
N]]) return(p) The Get_JN function finds the trigonometric polynomial
of order N for the function f.
The symbol of the sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] is the trigonometric polynomial
The Ij and Wr were ordered by sampling date (t) and gender, and a Fourier trigonometric polynomial
(Rey Pastor et al., 1987) using the least--squares technique was fitted:
To find expressions for both r(t) and s(t) (and assuming they have a trigonometric polynomial
which is just the trigonometric polynomial
in Weierstrass's first approximation theorem.