Zeev Ditzian

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For trigonometric polynomials on [−, ] ≡ T , the classical Jackson inequality E n (f) p C r (f, 1/n) p was sharpened by M. Timan for 1 < p < ∞ to yield n −r n k=1 k sr−1 E k (f) s p 1/s C r (f, n −1) p where s = max(p, 2). In this paper a general result on the relations between systems or sequences of best approximation and appropriate measures of(More)
The rate of convergence of Poisson sums and their combinations are shown to be equivalent to appropriate K-functionals. For a function f that has the expansion (1) f (x) ∼ ∞ k=0 P k (f) the Poisson sum is given by (2) A r f = ∞ k=0 r k P k (f), 0 < r < 1. For A r f to be written as a semi-group, we set r = e −t and obtain (3) T (t)f = ∞ k=0 e −kt P k (f).(More)