We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sp...

We will show that for any two bounded linear operators X, Y on a Hilbert space H, if they satisfy the triangle equality |X + Y | = |X | + |Y |, there exists a partial isometry U on H such that X = U |X | and Y = U |Y |. This is a generalization of Thompson’s theorem to the matrix case proved by using a trace. 47A05, 47A10, 47A12 operator theory, Hilbert space, triangle inequality

We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e. in the so-called Bianchi-CartanVranceanu family. This gives a positive answer to a conjecture formulated in [2]. As a partial result, we prove that totally umbilical surfaces only exist if the space is a Riemannian product of a surface of constant Ga...

An efficient algorithm for isometry-invariant matching of surfaces is presented. The key idea is computing the minimum-distortion mapping between two surfaces. For this purpose, we introduce the generalized multidimensional scaling, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another. The generalized multidimension...

The purpose of this note is to review and reorganize the proof of the Herwig–Lascar extension theorem, [2, Theorem 3.2], and to indicate how small additions to this proof can be used to obtain a sharper version of this theorem (Theorem 1.1 below) that is of some interest in applications, for example to the structure of isometry groups; see below. Let P be a family of partial bijections between ...

We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra A C of the cylinder, and an isomorphism between the free module A C and its direct sum A C ⊕ F C with the Fock module on the cylinder. We cons...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

Complete or partial rupture of the cranial cruciate ligament (CCL) is a common injury of the canine stifle. While numerous techniques have been developed for surgical treatment, extra-articular methods with placement of a lateral suture remain a popular treatment method. The purpose of this study was to determine the potential isometry of the six suture-paired sites; two on the femur and three ...