Spectral tetris is a flexible and elementary method to derive unit norm frames with a given frame operator having all of its eigenvalues ≥ 2. One important application of this method is to construct fusion frames. We will give necessary and sufficient conditions for a spectral tetris construction to give a fusion frame with prescribed eigenvalues for its fusion frame operator and with prescribe...

We present a new approach to sampling theory using the operator theory framework. We use a replacement operator and replace general frames of the sampling and reconstruction subspaces by normalized tight frames. The replacement can be done in a numerically stable and efficient way. The approach enables us to unify the standard consistent reconstruction results with the results for quasiconsiste...

In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...

the main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. the methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [b. r. yahaghi, near triangularizability implies triangularizability, canad. math. bull. 47, (2004), no. 2...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Fusion frames are generalizations of classical frames that provide a richer description of signal spaces where subspaces are used in the place of vectors as signal building blocks. The main idea of this work is to extend ideas from Compressed Sensing (CS) to a fusion frame setup. We use a sparsity model for fusion frames and then show that sparse signals under this model can be compressively sa...

Let H be a (separable) Hilbert space and {ek}k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled projections, and to obtain a new characteri...

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L 2 (G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Ries...

The bracket map was originally considered in [7] for locally compact abelian groups. In this work we extend the study of bracket maps to the noncommutative setting, providing characterizations of bases and frames for cyclic subspaces of the Heisenberg group. We also indicate how to generalize these results to a class of non-abelian nilpotent Lie groups whose irreducible representations are squa...