국소성과 프레임
Localization property and frames
- 주제(키워드) frames + localization property
- 발행기관 아주대학교
- 지도교수 하영화
- 발행년도 2006
- 학위수여년월 2006. 2
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 본문언어 영어
초록/요약
Localization of sequences with respect to Riesz bases for Hilbert spaces are comparable with perturbation of Riesz bases or frames. Gr\"{o}chenig first introduced the notion of localization. In this thesis, we introduce more general definition of localization and show that exponentially localized sequences and polynomially localized sequences with respect to Riesz bases are Bessel sequences. Furthermore, they are frames provided some additional conditions are satisfied.
more목차
Abstract ... 1
1. Introduction ... 2
2. Preliminaries ... 4
2.1 Bases in Banach space ... 4
2.2 Bessel sequences in Hilbert spaces ... 6
2.3 Riesz bases in Hilbert spaces ... 12
2.4 Frames ... 17
2.5 Frames versus Riesz bases ... 23
3. Localization property and frames ... 26
3.1 Gr\"{o}chenig 's definition ... 26
3.2 Localization equivalent to Gr\"{o}chenig 's definition
... 27
3.3 Generalized localization ... 37
3.4 Examples ... 46
Bibliography
