A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS
2010 ◽
Vol 08
(01)
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pp. 49-59
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Keyword(s):
This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L2(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L2(ℝn) to L2(G).
2013 ◽
Vol 11
(06)
◽
pp. 1392001
2020 ◽
Vol 18
(04)
◽
pp. 2050019
2011 ◽
Vol 48
(5)
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pp. 899-912
Keyword(s):
2016 ◽
Vol 15
(04)
◽
pp. 1650074
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1968 ◽
Vol 9
(2)
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pp. 98-100
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Keyword(s):
Keyword(s):
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