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A general quadrature formula using zeros of spherical Bessel functions as nodes

Riadh Ben Ghanem, Clément Frappier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We obtain, for entire functions of exponential type satisfying certain integrability conditions, a quadrature formula using the zeros of spherical Bessel functions as nodes. We deduce from this quadrature formula a result of Olivier and Rahman, which refines itself a formula of Boas.

A gradient-projective basis of compactly supported wavelets in dimension n > 1

Guy Battle (2013)

Open Mathematics

A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum χ ( n f · W χ * ) W χ converges to f with respect to the norm ( · ) L 2 ( n ) . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such that [...]...

A Korovkin type approximation theorems via -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

Using the concept of -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

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