THE RECOVERY OF FUNCTIONS OF PALEY-WIENER CLASS FROM IRREGULAR SAMPLINGS

【摘要】 <正>It is shown that a function f which is in the classical Paley-Wiener class, and its k-th derivative f(k) can be recovered in the metric Lq(R),2 < q ≤ ∞, from its values on irregularly distributed discrete sampling set {tj}j∈z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj}j∈z is a real sequence such that {eifj(?)}j∈z constitutes a Riesz basis for L2([-π,π]).更多还原

【Abstract】 It is shown that a function / which is in the classical Paley-Wiener class, and its k-th derivative f(k) can be recovered in the metric Lq(R),2 < q ≤∞, from its values on irregularly distributed discrete sampling set {tj}j∈Z as limits of polynomial spline interpolation when the order of the splines goes to infinity, where {tj }j∈Z is a real sequence such that {eitj(?)}j∈Z constitutes a Riesz basis for L2([-π,π]).更多还原