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A formula for the Bloch norm of a C 1 -function on the unit ball of n

Miroslav Pavlović (2008)

Czechoslovak Mathematical Journal

For a C 1 -function f on the unit ball 𝔹 n we define the Bloch norm by f 𝔅 = sup d ˜ f , where d ˜ f is the invariant derivative of f , and then show that f 𝔅 = sup z , w 𝔹 z w ( 1 - | z | 2 ) 1 / 2 ( 1 - | w | 2 ) 1 / 2 | f ( z ) - f ( w ) | | w - P w z - s w Q w z | .

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.

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