Inequalities for Fourier transforms
Some new inequalities of Ostrowski-Grüss type are derived. They are applied to the error analysis for some Gaussian and Gaussian-like quadrature formulas.
We study weighted -integrability (1 ≤ p < ∞) of trigonometric series. It is shown how the integrability of a function with weight depends on some regularity conditions on Fourier coefficients. Criteria for the uniform convergence of trigonometric series in terms of their coefficients are also studied.
We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.
We propose a two point subdivision scheme with parameters to draw curves that satisfy Hermite conditions at both ends of [a,b]. We build three functions f,p and s on dyadic numbers and, using infinite products of matrices, we prove that, under assumptions on the parameters, these functions can be extended by continuity on [a,b], with f'=p and f''=s .