Shift-modulation invariant spaces on LCA groups

Carlos Cabrelli, and Victoria Paternostro. "Shift-modulation invariant spaces on LCA groups." Studia Mathematica 211.1 (2012): 1-19. <http://eudml.org/doc/285748>.

@article{CarlosCabrelli2012,
abstract = {A (K,Λ) shift-modulation invariant space is a subspace of L²(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed subgroups of G and the dual group Ĝ, respectively. We provide a characterization of shift-modulation invariant spaces when K and Λ are uniform lattices. This extends previous results known for $L²(ℝ^\{d\})$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.},
author = {Carlos Cabrelli, Victoria Paternostro},
journal = {Studia Mathematica},
keywords = {shift-modulation invariant space; LCA group; range function; fiber},
language = {eng},
number = {1},
pages = {1-19},
title = {Shift-modulation invariant spaces on LCA groups},
url = {http://eudml.org/doc/285748},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Carlos Cabrelli
AU - Victoria Paternostro
TI - Shift-modulation invariant spaces on LCA groups
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 1
SP - 1
EP - 19
AB - A (K,Λ) shift-modulation invariant space is a subspace of L²(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed subgroups of G and the dual group Ĝ, respectively. We provide a characterization of shift-modulation invariant spaces when K and Λ are uniform lattices. This extends previous results known for $L²(ℝ^{d})$. We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.
LA - eng
KW - shift-modulation invariant space; LCA group; range function; fiber
UR - http://eudml.org/doc/285748
ER -