On the Density Condition of a Multiresolution Analysis in Lebesgue Spaces
We are interested in the problem of when the density condition in a multiresolution analysis defined in L p ( R n ) , 1 ≤ p ≤ ∞ , holds. Indeed, if 2 ≤ p < ∞ , we obtain sufficient conditions on the generators of a multiresolution analysis in order to the density condition is satisfied. We emphas...
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Published in | Mediterranean journal of mathematics Vol. 14; no. 3; pp. 1 - 13 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.06.2017
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | We are interested in the problem of when the density condition in a multiresolution analysis defined in
L
p
(
R
n
)
,
1
≤
p
≤
∞
, holds. Indeed, if
2
≤
p
<
∞
, we obtain sufficient conditions on the generators of a multiresolution analysis in order to the density condition is satisfied. We emphasis on the requirement of the Fourier transform in a neighborhood of the origin. This involves the notion of density point. When
1
≤
p
≤
2
, the obtained condition is necessary. Moreover, we study the same problem when a multiresolution analysis is defined in the subspace of
L
∞
(
R
n
)
of the set of all continuous functions vanishing at infinite. |
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ISSN: | 1660-5446 1660-5454 |
DOI: | 10.1007/s00009-017-0908-8 |