Dynamical sampling: mixed frame operators, representations and perturbations

E. Rashidi; A. Najati; E. Osgooei

Dynamical sampling: mixed frame operators, representations and perturbations

E. Rashidi, A. Najati, E. Osgooei

University of Mohaghegh Ardebili

Research output: Other contribution › Academic

Abstract

Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n \varphi\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n \varphi\}_{n=0}^{\infty}$.

Original language	Undefined/Unknown
Publication status	Published - 1 Apr 2019
Externally published	Yes

Cite this

@misc{a78b8d7b18e548cd8916a8bf4e2817bd,

title = "Dynamical sampling: mixed frame operators, representations and perturbations",

abstract = "Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n \varphi\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n \varphi\}_{n=0}^{\infty}$.",

author = "E. Rashidi and A. Najati and E. Osgooei",

year = "2019",

month = apr,

day = "1",

language = "Undefined/Unknown",

type = "Other",

}

TY - GEN

T1 - Dynamical sampling: mixed frame operators, representations and perturbations

AU - Rashidi, E.

AU - Najati, A.

AU - Osgooei, E.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n \varphi\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n \varphi\}_{n=0}^{\infty}$.

AB - Motivated by recent progress in operator representation of frames, we investigate the frames of the form $ \{T^n \varphi\}_{n\in I}$ for $ I=\mathbb{N}, \mathbb{Z} $, and answer questions about representations, perturbations and frames induced by the action of powers of bounded linear operators. As a particular case, we discuss problems concerning representation of frames in terms of iterations of the mixed frame operators. As our another contribution, we consider frames of the form $ \{a_n T^n \varphi\}_{n=0}^{\infty} $ for some non-zero scalars $ \{a_n\}_{n=0}^{\infty} $, and we obtain some new results in dynamical sampling. Finally, we will present some auxiliary results related to the perturbation of sequences of the form $ \{T^n \varphi\}_{n=0}^{\infty}$.

M3 - Other contribution

ER -