Abstract
Original language | English |
---|---|
Title of host publication | Operator Theory: Advances and Applications |
Volume | 268 |
Publisher | Springer |
Publication date | 2018 |
Pages | 155-165 |
ISBN (Print) | 9783319759968 |
DOIs | |
Publication status | Published - 2018 |
Series | Operator Theory |
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Volume | 268 |
ISSN | 0255-0156 |
Keywords
- Frames
- Dual frames
- Dynamical sampling
- Operator theory
Cite this
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Frames, operator representations, and open problems. / Christensen, Ole; Hasannasab, Marzieh.
Operator Theory: Advances and Applications. Vol. 268 Springer, 2018. p. 155-165 (Operator Theory, Vol. 268).Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
TY - CHAP
T1 - Frames, operator representations, and open problems
AU - Christensen, Ole
AU - Hasannasab, Marzieh
PY - 2018
Y1 - 2018
N2 - A frame in a Hilbert space H is a countable collection of elements in H that allows each f ϵ H to be expanded as an (infinite) linear combination of the frame elements. Frames generalize the wellknown orthonormal bases, but provide much more exibility and can often be constructed with properties that are not possible for orthonormal bases. We will present the basic facts in frame theory with focus on their operator theoretical characterizations and discuss open problems concerning representations of frames in terms of iterations of a fixed operator. These problems come up in the context of dynamical sampling, a topic that has recently attracted considerably interest within harmonic analysis. The goal of the paper is twofold, namely, that experts in operator theory will explore the potential of frames, and that frame theory will benefit from insight provided by the operator theory community.
AB - A frame in a Hilbert space H is a countable collection of elements in H that allows each f ϵ H to be expanded as an (infinite) linear combination of the frame elements. Frames generalize the wellknown orthonormal bases, but provide much more exibility and can often be constructed with properties that are not possible for orthonormal bases. We will present the basic facts in frame theory with focus on their operator theoretical characterizations and discuss open problems concerning representations of frames in terms of iterations of a fixed operator. These problems come up in the context of dynamical sampling, a topic that has recently attracted considerably interest within harmonic analysis. The goal of the paper is twofold, namely, that experts in operator theory will explore the potential of frames, and that frame theory will benefit from insight provided by the operator theory community.
KW - Frames
KW - Dual frames
KW - Dynamical sampling
KW - Operator theory
U2 - 10.1007/978-3-319-75996-8_8
DO - 10.1007/978-3-319-75996-8_8
M3 - Book chapter
SN - 9783319759968
VL - 268
SP - 155
EP - 165
BT - Operator Theory: Advances and Applications
PB - Springer
ER -