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1 Sep 2011: The general problem is to nd the complete collection G = f(A;B)g of sharpconstants in (1.1) which are dened as(1.2) A A0 := inf(;)2 ; B := ... Bojanov, ed.), SCT Publishing, 1994, pp. 192{204.5. S. B. Stechkin, Best approximation of linear operators,

22 Nov 2011: In other words, we wish to recover f L2(b,b) from pointwise samples of its Fourier transform. ... Ff(t) =. (b,b)f(x)e2πitx dx, t R. Specifically, we shall be interested in reconstructions from theequispaced samples.

1 Sep 2011: f(x) :=. k3. i=0. αii! (x a)i 1. (k 3)! b. ... g =. {h, on [a, b) ,p, on [b, b δ].

1 Sep 2011: 2.2.2 The matrices B, B′, C. Setyν := D(hν )qν, ν < N; yN := D(hN1)qN,. ... By definition (2.2.9),. C := CNν := ADγ1ADγ2 ADγN ν A,B := Bν := ADδ1ADδ2 ADδν ,B′ := B′ν := D0BD0,.

10 Oct 2011: D(g) =(D̂(g) B(g). 0 C(g). )for u =. (û0. ), (1.19). ... v1,v2) a. (e2πki. n v1,e 2πki. n v2) = (v1,v2)A, (v1,v2) b.