On Weaving Generalized Frames and Generalized Riesz Bases

被引：0
作者：
Aniruddha Deepshikha
机构：
[1] University of Calcutta,Department of Mathematics, Shyampur Siddheswari Mahavidyalaya
[2] Indian Institute of Technology Kharagpur,Department of Mathematics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2022年 / 45卷
关键词：
Hilbert frames; Frame operator; Generalized frames; Riesz bases; Weaving frames; 42C15; 42C30; 42C40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Weaving frames have potential applications in wireless sensor networks that require distributed processing of signals under different frames. In this paper, we study some new properties of weaving generalized frames (or g-frames) and weaving generalized orthonormal bases (or g-orthonormal bases). It is shown that a g-frame and its dual g-frame are woven. The inter-relation of optimal g-frame bounds and optimal universal g-frame bounds is studied. Further, we present a characterization of weaving g-frames. Illustrations are given to show the difference in properties of weaving generalized Riesz bases and weaving Riesz bases.
引用
收藏
页码：361 / 378
页数：17
相关论文
共 35 条
  • [1] Bemrose T(2016)Weaving frames Oper. Matrices 10 1093-1116
  • [2] Casazza PG(2016)Weaving Schauder frames J. Approx. Theory 211 42-60
  • [3] Gröchenig K(2004)Frames of subspaces Contemp. Math. 345 87-114
  • [4] Lammers MC(1986)Painless nonorthogonal expansions J. Math. Phys. 27 1271-1283
  • [5] Lynch RG(2018)On weaving frames Houston J. Math. 44 887-915
  • [6] Casazza PG(2018)Vector-valued (super) weaving frames J. Geom. Phys. 134 48-57
  • [7] Freeman D(1952)A class of nonharmonic Fourier series Trans. Am. Math. Soc. 72 341-366
  • [8] Lynch RG(2004)Quasi-orthogonal decompositions of structured frames J. Math. Anal. Appl. 289 80-199
  • [9] Casazza PG(2000)Frames, bases and group representations Mem. Am. Math. Soc. 147 1-94
  • [10] Kutyniok G(2019)Weaving Bull. Malays. Math. Sci. Soc. 42 3111-3129
1234