In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Abstract In the paper, we study approximation properties of Malmquist-Takenaka-Christov (MTC) system. We show that discrete MTC approximations converge rapidly under mild restrictions on functions asymptotic at infinity. This makes them particularly suitable for solving semi- and quasi-linear problems containing Fourier multipliers, whose symbols are not smooth origin. As a concrete application...

The rational meromorphic functions on $\mathbb{C}\backslash\mathbb{R}$ are studied. We consider the some classes of one, as generalized Nevanlinna $\mathbf{N}_{\kappa}$ and Stieltjes $\mathbf{N}_{\kappa}^{k}$ classes. By Euclidean algorithm, we can find indices $\kappa$ $k$, i.e. determine which class function belongs to $\mathbf{N}_{\kappa}^{k}$.

We show that every inner divisor of the operator-valued coordinate function, zIE, is a Blaschke-Potapov factor. also introduce notion “rational” function and then Δ two-sided rational if only it can be represented as finite product; this extends to functions well-known result proved by V.P. Potapov for matrix-valued functions.

A rational function can always be integrated, that is, the integral of such a is an elementary function. The integration procedure complex and consists four steps: elimination common zero-points numerator denominator, reduction to true function, decomposition into partial fractions obtained expressions using direct integration, substitution method or method. Integrating functions important beca...