Besselovi nizovi i bazni okviri

Perišić, Marija Majda (2014) Besselovi nizovi i bazni okviri. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

This thesis consists of three parts. The first part contains definitions and important results of the theory of normed vector spaces which will be used to describe Bessel sequences and frames. In the second, central part of the thesis, we present properties and characterizations of Bessel sequences and frames. We describe duals and dual frames and show main results concerning them. Furthermore, we make a comparison of frames and bases and state the equivalence of exact, Parsel frames and orthonormal bases. Finally, we study tight frames and highlight Parsel frames. In chapter three we state necessary and sufficient condition under which a Bessel sequence can be extended to a frame by adding a finite sequence of vectors. In the same spirit, we provide necessary and sufficient condition for the existence of a finite extension of a Bessel sequence to a Parsel frame.

Item Type: Thesis (Diploma thesis)
Supervisor: Bakić, Damir
Date: 2014
Number of Pages: 49
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 16 Jun 2015 10:36
Last Modified: 16 Jun 2015 10:36
URI: http://digre.pmf.unizg.hr/id/eprint/4052

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