Infinite matrices, wavelet coefficients and frames.
Inhomogenous RefinementEquations.
Integrability and continuity of functions represented by trigonometric series: coefficients criteria
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.
Integral inequalities of the Ostrowski type.
Integral Kernels and Approximation on Totally Real Submanifolds of Cn.
Integral representations for Padé-type operators.
Integration of polynomials
We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.
Integration over a Simplex, Truncated Cubes, and Eulerian Numbers.
Intégrité du complété et théorème de Stone-Weierstrass
Interpolace — vývoj formulace problému a jeho řešení
Interpolación, eliminación y matrices totalmente positivas.
Interpolación funcional en Rn.
Interpolants d’Hermite obtenus par subdivision
Interpolants d'Hermite C2 obtenus par subdivision
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 .
Interpolating and smoothing biquadratic spline
The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and...
Interpolating bases for spaces of differentiable functions
Interpolating the m-th power of x at the zeros of the n-th Chebyshev-polynomial yields an almost best Chebyshev-approximation.
Interpolation and integration based on averaged values
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
Interpolation and the Laguerre-Pólya class.
Interpolation by bivariate polynomials based on Radon projections
For any given set of angles θ₀ < ... < θₙ in [0,π), we show that a set of Radon projections, consisting of k parallel X-ray beams in each direction , k = 0, ..., n, determines uniquely algebraic polynomials of degree n in two variables.