This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /splâ€¦ (More)

Suppose we wish to recover a vector x0 âˆˆ R (e.g. a digital signal or image) from incomplete and contaminated observations y = Ax0 + e; A is a n by m matrix with far fewer rows than columns (n â‰ª m)â€¦ (More)

Suppose we are given a vector f in a class FsubeRopf<sup>N </sup>, e.g., a class of digital signals or digital images. How many linear measurements do we need to make about f to be able to recover fâ€¦ (More)

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = XÎ² + z, where Î² âˆˆ R isâ€¦ (More)

We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n 4) and the SchrÃ¶dinger equation (in dimension n 3).â€¦ (More)

A very old and fundamental question about the representation theory of GLn(C) is the following: For which triples of dominant weights Î», Î¼, Î½ does the tensor product VÎ»âŠ—VÎ¼âŠ—VÎ½ of the irreducibleâ€¦ (More)

Let A be a subset of a finite field F := Z/qZ for some prime q. If |F | Î´ < |A| < |F | 1âˆ’Î´ for some Î´ > 0, then we prove the estimate |A + A| + |A Â· A| â‰¥ c(Î´)|A| 1+Îµ for some Îµ = Îµ(Î´) > 0. This is aâ€¦ (More)

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. [. . . ] [. . . ] for all x âˆˆ ZN (here (m0, t0, L0) = (3, 2, 1)) and E ( Î½((xâˆ’â€¦ (More)