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Interpolation Processes: Basic Theory and Applications
The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors… Expand
Weighted Polynomial Inequalities with Doubling and A∞ Weights
Abstract. We consider weighted inequalities such as Bernstein, Nikolskii, Remez, etc., inequalities under minimal assumptions on the weights. It turns out that in most cases this mimimal assumption… Expand
Lagrange Interpolation at Laguerre Zeros in Some Weighted Uniform Spaces
We introduce an interpolatory process essentially based on the Laguerre zeros and we prove that it is an optimal process in some weighted uniform spaces.
Nyström interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations
We consider a special class of Wiener-Hopf integral equations u(y) - λ ∫ 0 ∞ h(y - x)u(x) dx = f(y), with || ∫ 0 ∞ |h(y - x)|dx||∞ < λ -1 , whose solutions u(x) decay exponentially at infinity. First… Expand
POLYNOMIAL APPROXIMATION ON THE REAL SEMIAXIS WITH GENERALIZED LAGUERRE WEIGHTS
We present a complete collection of results dealing with the polynomial approximation of functions on (0,+1).
Nyström interpolants based on the zeros of Legendre polynomials for a non-compact integral operator equation
We consider two different Nystrom interpolants for the numerical solution of the following singular integral equation (formule...), 0 < x ≤ 1, arising from a problem of determining the distribution… Expand
On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals
SummaryIn a previous paper the authors proposed a modified Gaussian ruleФ*m(wf;t)to compute the integral Π(wf;t) in the Cauchy principal value sense associated with the weightw, and they proved the… Expand
Projection Methods and Condition Numbers in Uniform Norm for Fredholm and Cauchy Singular Integral Equations
In this paper the authors propose a numerical method for the approximate solution of some classes of Fredholm and Cauchy integral equations including "discrete collocation" and "collocation" methods. Expand
Some numerical methods for second-kind Fredholm integral equations on the real semiaxis
In this paper we introduce some numerical methods for solving Fredholm integral equations of the second kind on the real semiaxis and prove that the proposed procedures are stable and convergent.… Expand
Best Approximation and Moduli of Smoothness for Doubling Weights
In this paper we relate the rate of weighted polynomial approximation to some weighted moduli of smoothness for so-called doubling weights. Expand