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5 Oct 2013: The well known NS-Sampling Theorem [24, 26, 29, 30, 34] states that if.

5 Oct 2013: Stable reconstructions in Hilbert spaces and the resolutionof the Gibbs phenomenon. Ben AdcockDepartment of Mathematics. Simon Fraser UniversityBurnaby, BC V5A 1S6. Canada. Anders C. HansenDAMTP, Centre for Mathematical Sciences. University of

5 Oct 2013: xm} is a grid of mequispaced points in [1, 1]. In [24] it was shown that. ... Proc. SPIE, 7535, 2010. [24] D. Coppersmith and T. Rivlin. The growth of polynomials bounded at equally spaced points.

5 Oct 2013: The problem is not new, and therehave been many different approaches developed for its solution (see, for example, [2, 11, 12, 17, 18, 22,23, 24, 25, 52] and references therein).

5 Oct 2013: A Theoretical Framework for Backward Error Analysis. on Manifolds. Anders C. HansenDAMTP, Centre for Mathematical Sciences. University of CambridgeWilberforce Rd, Cambridge CB3 0WA. United Kingdom. Abstract. Backward Error Analysis (BEA) has been a

5 Oct 2013: The second inclusion follows by Theorem VIII.24 ([RS72], p. 290)if we can show that PnAPn A in the strong resolvent sense. ... 11. Proof. Now, (i) follows from the fact that A1,n A strongly (see Theorem VIII.24 in [RS72],p.

5 Oct 2013: Indeed, one typically requiresan intolerably large number of samples m to recover f to any reasonably accuracy [13, 24]. ... 24]. Note in the case above that f has only m nonzerocoefficients in the basis {wj}jN.

5 Oct 2013: 3 Consistent reconstructions and oblique projections. We now consider the consistent sampling technique of [24, 25, 29, 56, 58]. ... An analysis of consistent reconstructions, which we shall recap and extend in 3.3, was given in[24, 25, 29].

5 Oct 2013: Thiswas later considered by Eldar et al, who extended this framework to frames in arbitrary Hilbert spaces[18, 19, 20, 24]. ... M2 =. C(γ)M11. 2. (24). Proof. Without loss of generality, in this proof, M1 and M2 will be even.

5 Oct 2013: R. Driscoll, “Wavelet-encodedMR imaging,” Magn. Reson. Med., vol. 24, pp. 275–287, 1992.