Convergence of Lagrange interpolation series in the Fock spaces
نویسندگان
چکیده
منابع مشابه
Convergence of Extended Lagrange Interpolation
The authors give a procedure to construct extended interpolation formulae and prove some uniform convergence theorems.
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It was shown by James Tung in 2005 that if a sequence Z = {zn} of points in the complex plane satisfies inf n6=m |zn − zm| > 2/ √ α, then Z is a sequence of interpolation for the Fock space F p α . Using results from circle packing, we show that the constant above can be improved to √ 2π/( √ 3α), which is strictly smaller than 2/ √ α. A similar result will also be obtained for sampling sequences.
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Quadrature convergence of the extended Lagrange interpolant L2n+1f for any continuous function f is studied, where the interpolation nodes are the n zeros τi of an orthogonal polynomial of degree n and the n+ 1 zeros τ̂j of the corresponding “induced” orthogonal polynomial of degree n + 1. It is found that, unlike convergence in the mean, quadrature convergence does hold for all four Chebyshev w...
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We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2014
ISSN: 0214-1493
DOI: 10.5565/publmat_58114_05