This paper follows the recent discussion on the sparse solution recovery with quasi-norms lq, q ∈ (0, 1) when the sensing matrix possesses a Restricted Isometry Constant δ2k (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if δ2k ≤ 1/2, any minimizer of the lq minimization, at lea...

we consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion‎. ‎in particular, we prove a version of plancherel-po ́lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

This paper studies four families of polyhedral norms parametrized by a single parameter. The first two families consist of the CVaR norm (which is equivalent to the D-norm, or the largest-k norm) and its dual norm, while the second two families consist of the convex combination of the l1and l∞-norms, referred to as the deltoidal norm, and its dual norm. These families contain the l1and l∞-norms...

We develop a unified approach to proving Lp−Lq boundedness of spectral projectors, the resolvent Laplace-Beltrami operator and its derivative on Hd. In case when p q are in duality, dependence implicit constant is shown be sharp. also give partial results question Fourier extension operator. As an application, we prove smoothing estimates for free Schrödinger equation Hd limiting absorption pri...

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion‎. ‎In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper an alternative version of the Riccati recursion solver for LQ control problems is presented. The performanc...

Consider the standard linear regression model Y = Xβ+w, where Y ∈ R is an observation vector, X ∈ R is a design matrix, β ∈ R is the unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimation of β for lp-losses and in the l2-prediction loss, assuming that β belongs to an lq-ball Bq(Rq) for some q ∈ [0, 1]. We show ...