Dirichlet polynomials in connection with Φ-widths and compressed sensing 

B. Kashin (Steklov Math. Inst., Moscow) 
April 4, 2013, 2:45 p.m.

Let Φ= {ϕi} be a system of elements of a Banach space X. We deﬁne Φ-width of order N of the set A ⊂ X as a value of the optimal approximation (with respect to norm in X) of the set A by the subspace generated by N arbitrary elements of the system Φ. In the case when Φ is a trigonometric system, this notion was introduced in 1974 by R. Ismagilov. The talk is devoted to the Φ-width estimates, their connections with “compressed sensing,” and their application to the investigations of “polynomials” with respect to the system  {nit} . 
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