We apply Lax-Milgram theorem to characterize scalable and piecewise frame in finite infinite-dimensional Hilbert spaces. also introduce a method for approximating the inverse operator using finite-dimensional linear algebra which, best of our knowledge, is new literature.

This paper presents the three topologies of three-phase four-wire DSTATCOM for reduction of harmonics, reactive power compensation, increasing power factor, which occur due to a nonlinear load, environment problem and polluted grid. The performances of the above topologies have been compared for the magnitude of source current, power factor improvement, DC-link voltage regulation, and total har...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential. The definition of the DFT requires associated uncertainty principle inequalities. The definition of the ambiguity function requires a component that leads to ...

Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to ...

Title of dissertation: FRAME MULTIPLICATION THEORY FOR VECTOR-VALUED HARMONIC ANALYSIS Travis D. Andrews, Doctor of Philosophy, 2014 Dissertation directed by: Professor John J. Benedetto Department of Mathematics A tight frame Φ is a sequence in a separable Hilbert space H satisfying the frame inequality with equal upper and lower bounds and possessing a simple reconstruction formula. We define...