piecewise approximation

Discrete Transform with Stick Property Based on {sinx sinkx} and Second Kind Chebyshev Polynomials Systems

Authors: Sharapudinov I. I., Akniev G. G.

In this paper we introduce the discrete series with the «sticking»-property of the periodic ({sinx sinkx} system) and non-periodic (using the system of the second kind of Chebyshev polynomials Uk(x)) cases. It is shown that series of the system {sinx sinkx}
have an advantage over cosine Fourier series because they have better approximation properties near the bounds of the [0, π] segment. Similarly discrete series of the system Uk(x) near the bound of the [−1, 1] approximates given function significantly

Some Special Two-dimensional Series of {sinx sinkx} System and Their Approximation Properties

Authors: Sharapudinov I. I.

In present paper there were introduced two-dimensional special series of the system {sinx sinkx}. It’s shown that these series have the advantage over two-dimensional cosine Fourier series, because they have better approximation properties near the bounds of the square [0, 1]2. It’s given convergence speed estimate of special series partial sums to functions f(x, y) from the space of even 2π-periodic continuous functions.