Weighted l1-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In this work, we study the recovery conditions and the associated recovery guarantees of weighted l1-minimization when arbitrarily many distinct weights are permitted. ...

Weighted l1-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In this work, we study the recovery conditions and the associated recovery guarantees of weighted l1-minimization when arbitrarily many distinct weights are permitted. ...

It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t)= c(t)u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented. Isometries in complex function spaces have been studied successfully ...

In this note we present two new positive answers to Tingley’s problem in certain subspaces of function algebras. the first result prove that every surjective isometry between unit spheres, S(A) and S(B), uniformly closed algebras A B on locally compact Hausdor? spaces can be extended a real linear from onto B. second part study isometries spheres abelian JB*-triples represented as continuous fu...