Frames for Metric Spaces

被引：1

作者：

Krishna, K. Mahesh ^{[1
]}

Johnson, P. Sam ^{[2
]}

机构：

[1] Indian Stat Inst, Bangalore Ctr, Stat Math Unit, Bangalore 560059, Karnataka, India

[2] Natl Inst Technol Karnataka NITK, Dept Math & Computat Sci, Surathkal 575025, Mangaluru, India

来源：

RESULTS IN MATHEMATICS | 2022年 / 77卷 / 01期

关键词：

Frame; metric space; Lipschitz function; INTEGRABLE GROUP-REPRESENTATIONS; BANACH FRAMES; P-FRAMES; ATOMIC DECOMPOSITIONS; COORBIT THEORY; PERTURBATION; PROPERTY;

D O I：

10.1007/s00025-021-01583-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric M-d-frame. Through Lipschitz-free Banach spaces we show that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. We derive some characterizations of metric frames. We also derive stability results for metric frames.

引用

页数：30

共 56 条

[1] p-frames and shift invariant subspaces of LP [J].

Aldroubi, A ;

Sun, Q ;

Tang, WS .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2001, 7 (01) :1-21

[2] PORTRAITS OF FRAMES [J].

ALDROUBI, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (06) :1661-1668

[3] Slanted matrices, Banach frames, and sampling [J].

Aldroubi, Akram ;

Baskakov, Anatoly ;

Krishtal, Ilya .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (07) :1667-1691

[4]

[Anonymous], 2013, Finite Frames Theory and Applications. Applied and Numerical Harmonic Analysis, DOI DOI 10.1007/978-0-8176-8373-3

[5] Equivalence relations and distances between Hilbert frames [J].

Balan, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (08) :2353-2366

[6]

Bana J., 2014, SEQUENCE SPACES MEAS

[7] Frame decomposition of decomposition spaces [J].

Borup, Lasse ;

Nielsen, Morten .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2007, 13 (01) :39-70

[8] The reconstruction formula for Banach frames and duality [J].

Carando, Daniel ;

Lassalle, Silvia ;

Schmidberg, Pablo .

JOURNAL OF APPROXIMATION THEORY, 2011, 163 (05) :640-651

[9] Duality, reflexivity and atomic decompositions in Banach spaces [J].

Carando, Daniel ;

Lassalle, Silvia .

STUDIA MATHEMATICA, 2009, 191 (01) :67-80

[10] Frame expansions in separable Banach spaces [J].

Casazza, P ;

Christensen, O ;

Stoeva, DT .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 307 (02) :710-723

← 1 2 3 4 5 6 →