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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 generalization of Radó's theorem

E. M. Chirka (2003)

Annales Polonici Mathematici

If Σ is a compact subset of a domain Ω ⊂ ℂ and the cluster values on ∂Σ of a holomorphic function f in Ω∖Σ, f' ≢ 0, are contained in a compact null-set for the holomorphic Dirichlet class, then f extends holomorphically onto the whole domain Ω.

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