The theory of reproducing systems on locally compact abelian groups

Gitta Kutyniok, and Demetrio Labate. "The theory of reproducing systems on locally compact abelian groups." Colloquium Mathematicae 106.2 (2006): 197-220. <http://eudml.org/doc/286281>.

@article{GittaKutyniok2006,
abstract = {A reproducing system is a countable collection of functions $\{ϕ_\{j\}: j ∈ \}$ such that a general function f can be decomposed as $f = ∑_\{j∈\} c_\{j\}(f)ϕ_\{j\}$, with some control on the analyzing coefficients $c_\{j\}(f)$. Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G). As an application, we obtain a new characterization of Parseval frame generators for Gabor and affine systems on L²(G).},
author = {Gitta Kutyniok, Demetrio Labate},
journal = {Colloquium Mathematicae},
keywords = {locally compact Abelian group; duality; Plancherel formula; frames; wavelets; Gabor systems; affine systems},
language = {eng},
number = {2},
pages = {197-220},
title = {The theory of reproducing systems on locally compact abelian groups},
url = {http://eudml.org/doc/286281},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Gitta Kutyniok
AU - Demetrio Labate
TI - The theory of reproducing systems on locally compact abelian groups
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 197
EP - 220
AB - A reproducing system is a countable collection of functions ${ϕ_{j}: j ∈ }$ such that a general function f can be decomposed as $f = ∑_{j∈} c_{j}(f)ϕ_{j}$, with some control on the analyzing coefficients $c_{j}(f)$. Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint in the study of reproducing systems on locally compact abelian groups G. This approach gives a novel characterization of the Parseval frame generators for a very general class of reproducing systems on L²(G). As an application, we obtain a new characterization of Parseval frame generators for Gabor and affine systems on L²(G).
LA - eng
KW - locally compact Abelian group; duality; Plancherel formula; frames; wavelets; Gabor systems; affine systems
UR - http://eudml.org/doc/286281
ER -