On Weaving Generalized Frames and Generalized Riesz Bases

被引：0
|
作者：
Deepshikha [1 ]
Samanta, Aniruddha [2 ]
机构：
[1] Univ Calcutta, Shyampur Siddheswari Mahavidyalaya, Dept Math, Kolkata 711312, India
[2] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2022年 / 45卷 / 01期
关键词：
Hilbert frames; Frame operator; Generalized frames; Riesz bases; Weaving frames;
D O I：
10.1007/s40840-021-01193-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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：18
相关论文
共 50 条
  • [1] On Weaving Generalized Frames and Generalized Riesz Bases
    Aniruddha Deepshikha
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2022, 45 : 361 - 378
  • [2] ON GENERALIZED WEAVING FRAMES IN HILBERT SPACES
    Vashisht, Lalit K.
    Garg, Saakshi
    Deepshikha
    Das, P. K.
    [J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2018, 48 (02) : 661 - 685
  • [3] Generalized Weaving Frames for Operators in Hilbert Spaces
    Lalit K. Deepshikha
    Geetika Vashisht
    [J]. Results in Mathematics, 2017, 72 : 1369 - 1391
  • [4] Generalized Weaving Frames for Operators in Hilbert Spaces
    Deepshikha
    Vashisht, Lalit K.
    Verma, Geetika
    [J]. RESULTS IN MATHEMATICS, 2017, 72 (03) : 1369 - 1391
  • [5] GENERALIZED CONTINUOUS K-WEAVING FRAMES
    Shipra
    Shekhar, Chander
    Chugh, Renu
    [J]. JORDAN JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 15 (4B): : 1111 - 1126
  • [6] Generalized Riesz Systems and Quasi Bases in Hilbert Space
    F. Bagarello
    H. Inoue
    C. Trapani
    [J]. Mediterranean Journal of Mathematics, 2020, 17
  • [7] Generalized Riesz Systems and Quasi Bases in Hilbert Space
    Bagarello, F.
    Inoue, H.
    Trapani, C.
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (02)
  • [8] ON THE STABILITY OF FRAMES AND RIESZ BASES
    FAVIER, SJ
    ZALIK, RA
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1995, 2 (02) : 160 - 173
  • [9] Semi-regular biorthogonal pairs and generalized Riesz bases
    Inoue, H.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2016, 57 (11)
  • [10] Weaving properties of generalized continuous frames generated by an iterated function system
    Vashisht, L. K.
    Deepshikha
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2016, 110 : 282 - 295
12345