We develope a local theory for frames on finite dimensional Hilbert spaces. We show that for every frame (fi) m i=1 for an n-dimensional Hilbert space, and for every ǫ > 0, there is a subset I ⊂ {1, 2, . . . ,m} with |I| ≥ (1 − ǫ)n so that (fi)i∈I is a Riesz basis for its span with Riesz basis constant a function of ǫ, the frame bounds, and (‖fi‖) m i=1 , but independent of m and n. We also con...

We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vector in an arbitrary Riesz basis from sufficiently many of its samples in any other Riesz basis. This framework can be viewed as an extension of the well-known consistent reconstruction technique (Eldar et al). However,...

The boundedness of Bessel–Riesz operators defined on Lebesgue spaces and Morrey in measure metric is discussed this research study. maximal operator traditional dyadic decomposition are used to study the Bessel-Riesz operators. We investigate interaction between kernel space parameters get results see how affects kernel-bound

Texture-based computerized analysis of high-resolution computed tomography images from patients with interstitial lung diseases is introduced to assist radiologists in image interpretation. The cornerstone of our approach is to learn lung texture signatures using a linear combination of N-th order Riesz templates at multiple scales. The weights of the linear combination are derived from one-ver...

The Dirac operators Ly = i 1 0 0 −1 dy dx + v(x)y, y = y1 y2 , x ∈ [0, π], with L 2-potentials v(x) = 0 P (x) Q(x) 0 , P,Q ∈ L 2 ([0, π]), considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projections SN = 1 2πi |z|=N− 1 2 (z − L bc) −1 dz, Pn = 1 2πi |z−n|= 1 2 (z − L bc) −1 dz are well-defined for |n| ≥ N if N is suffi...

A new class of positive definite functions related to colour-length function on arbitrary Coxeter group is introduced. Extensions of positive definite functions, called the Riesz-Coxeter product, from the Riesz product on the Rademacher (Abelian Coxeter) group to arbitrary Coxeter group is obtained. Applications to harmonic analysis, operator spaces and noncommutative probability is presented. ...

*Correspondence: [email protected] 3Faculty of Science and Technology, Tapee College, Surathani, 84000, Thailand Full list of author information is available at the end of the article Abstract In this paper, we obtain new Riesz representations of continuous linear maps associated with certain boundary value problems in the set of all closed bounded convex non-empty subsets of any Banach sp...

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

The aim of this paper is to study certain correlations between lower and upper bounds of exponential Riesz sequences, in particular between sharp lower and upper bounds, where we show that the product of the sharp bounds of an exponential Riesz sequence is bounded from above by a universal constant. The result is applied to the norms of coefficient and frame operators and their inverses.

We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main tool used in the proofs is the representation for a power of the farthest distance function as a Riesz potential of a unit Borel measure. MSC 2010. P...