Existence of Parseval oblique duals of a frame sequence

被引：2
|
作者：
Koo, Yoo Young [1 ]
Lim, Jae Kun [2 ]
机构：
[1] Yonsei Univ, Univ Coll, Seoul 120749, South Korea
[2] Hankyong Natl Univ, Dept Appl Math, Anseongsi 456749, Gyeonggido, South Korea
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 404卷 / 02期
基金：
新加坡国家研究基金会;
关键词：
Frame; Frame sequence; Oblique dual; Excess; Isometry; SPACES;
D O I：
10.1016/j.jmaa.2013.03.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a collection of necessary and sufficient conditions for the existence of a Parseval oblique dual (in an appropriate subspace) of a frame sequence. This result extends the previous results by Han and Larson, Antezana et al. and Han. Our proof shows that the problem is closely related with that of extending an operator with norm less than or-equal to 1 to an isometry on a subspace. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：470 / 476
页数：7
相关论文
共 50 条
  • [1] Applications of Parameterizations of Oblique Duals of a Frame Sequence
    Kim, Hyoungseok
    Koo, Yoo Young
    Lim, Jae Kun
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2013, 34 (08) : 896 - 913
  • [2] Frame representations and Parseval duals with applications to Gabor frames
    Han, Deguang
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (06) : 3307 - 3326
  • [3] Gabor frame multipliers and Parseval duals on the half real line
    Yang, Ming
    Li, Yun-Zhang
    INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2024, 22 (04)
  • [4] Parseval frame scaling sets and MSF Parseval frame wavelets
    Liu, Zhanwei
    Hu, Guoen
    Lu, Zhibo
    CHAOS SOLITONS & FRACTALS, 2009, 41 (04) : 1966 - 1974
  • [5] Approximate duals and nearly Parseval frames
    Mirzaee Azandaryani, Morteza
    TURKISH JOURNAL OF MATHEMATICS, 2015, 39 (04) : 515 - 526
  • [6] The Characterization of Parseval Frame Wavelets
    Xin Xiang ZHANGGuo Chang WU College of InformationHenan University of Finance and EconomicsHenan PRChina
    数学研究与评论, 2011, 31 (02) : 242 - 250
  • [7] The Characterization of Parseval Frame Wavelets
    Xin Xiang ZHANG
    Journal of Mathematical Research with Applications, 2011, (02) : 242 - 250
  • [8] Duals of Frame Sequences
    Heil, Christopher
    Koo, Yoo Young
    Lim, Jae Kun
    ACTA APPLICANDAE MATHEMATICAE, 2009, 107 (1-3) : 75 - 90
  • [9] Duals of Frame Sequences
    Christopher Heil
    Yoo Young Koo
    Jae Kun Lim
    Acta Applicandae Mathematicae, 2009, 107 : 75 - 90
  • [10] On Parseval super-frame wavelets
    LI Zhongyan SHI XianliangCollege of Mathematics and Computer ScienceKey Laboratory of High Performance Computing and Stochastic Information ProcessingHPCSIPMinistry of Education of China Hunan Normal UniversityChangsha ChinaDepartment of Mathematics and PhysicsNorth China Electric Power UniversityBeijing China
    Applied Mathematics:A Journal of Chinese Universities(Series B), 2012, 27 (02) : 192 - 204
12345