We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the l1-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and nu...

Given a spectral triple of compact type with a real structure in the sense of [Da̧browski L., J. Geom. Phys. 56 (2006), 86–107] (which is a modification of Connes’ original definition to accommodate examples coming from quantum group theory) and references therein, we prove that there is always a universal object in the category of compact quantum group acting by orientation preserving isometrie...

We prove that any isometry between the unit spheres of $C^2$-smooth (more generally, absolutely smooth) smooth Banach spaces extends to a linear spaces. This answers famous Tingley's problem in class $2$-dimensional

We give the complete classification of all sub-Riemannian model spaces with both step and rank three. Model in this context refer to where any infinitesimal isometry between horizontal tangent can be integrated a full isometry. They will divided into three families based on their nilpotentization. Each family depend different number parameters, making result crucially from known case two spaces...

This work presents an algorithm for the computation of canonical forms of linear codes over arbitrary finite chain rings under the action of the linear isometry group. It is a generalization of a previous work by the author on the canonization of linear codes over finite fields. The algorithm is based on the ideas of partition refinements and it will compute the automorphism group of the code a...

Title of dissertation: TENSOR COMPLETION FOR MULTIDIMENSIONAL INVERSE PROBLEMS WITH APPLICATIONS TO MAGNETIC RESONANCE RELAXOMETRY Ariel Hafftka, Doctor of Philosophy, 2016 Dissertation directed by: Professor Wojciech Czaja Department of Mathematics This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approxima...

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essent...

Let H be a Hilbert space with an inner product that is conjugate linear in the first variable. We do not presume unless we say so that H is separable. We denote by B(H) the set of bounded linear operators H → H. For any A ∈ B(H), A∗A is positive and one proves that it has a unique positive square root |A| ∈ B(H). We call |A| the absolute value of A. We say that U ∈ B(H) is a partial isometry if...

In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R...