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Keywords
(4)
Functional Form
Large Classes
riesz bases
riesz basis
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(1)
Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernel Hilbert Spaces
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Riesz Bases in Subspaces of L2 (R+ )
Riesz Bases in Subspaces of L2 (R+ ),10.1007/s003650010019,Constructive Approximation,Tim N. T. Goodman,Charles A. Micchelli,Zuowei Shen
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Riesz Bases in Subspaces of L2 (R+ )
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Citations: 2
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Tim N. T. Goodman
,
Charles A. Micchelli
,
Zuowei Shen
. In a recent investigation [8] concerning the asymptotic behavior of Gram—Schmidt orthonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system on . This result is applied to identify a large class of functions for which very general translates enjoy the
Riesz basis
property in .
Journal:
Constructive Approximation  CONSTR APPROX
, vol. 17, no. 1, pp. 3946, 2001
DOI:
10.1007/s003650010019
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Citation Context
(2)
...Similarly, whereas there are methods for generating Riesz bases in subspaces of L2(R) and L2(R+) [
13
, 18], we are not aware of general methods for generating Riesz bases in subspaces of L2(Rd) for d ≥ 2, except for grids of sampling points with, apart...
Cornelis V. M. van der Mee
,
et al.
A Method for Generating Infinite Positive Selfadjoint Test Matrices a...
...Using the corresponding sampling results on S = R and a recent result of Goodman et al. [
16
] on deriving Riesz bases of functions of the halfline...
...However, it will turn out that the sequence of unilateral translates {φ( ·− tj )}∞ j =0 is a Riesz basis of a suitable RKHS on R + which can be described explicitly in terms of Hardy spaces, if the sequence of bilateral translates {φ( ·− tj )}∞ j =−∞ is a Riesz basis of H P 2 . A major tool in deriving these results will be the main result of [
16
] which allows one to derive certain sampling expansions on RKHS of functions on R ...
...is bounded and strictly positive selfadjoint on � 2(Z+) or, equivalently, that the functions {φ( ·− tj )}j ∈Z+ on the positive halfline form a Riesz basis of a suitable closed subspace of the RKHS H P 2 defined in section 3.1. Its proof is based on [
16
], theorem 2.4...
...Proof. In view of theorem 2.4 of Goodman et al. [
16
] and theorem 3.2 above, it suffices to prove the following: (i) The functions {φ(·−tj )}j ∈Z+ form a Riesz basis of some closed subspace of L2(R)...
Cornelis V. M. Van Der Mee
,
et al.
Sampling Expansions and Interpolation in Unitarily Translation Invaria...
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Citations
(2)
A Method for Generating Infinite Positive Selfadjoint Test Matrices and Riesz Bases
(
Citations: 6
)
Cornelis V. M. van der Mee
,
Sebastiano Seatzu
Journal:
Siam Journal on Matrix Analysis and Applications  SIAM J MATRIX ANAL APPLICAT
, vol. 26, no. 4, pp. 11321149, 2005
Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernel Hilbert Spaces
(
Citations: 8
)
Cornelis V. M. Van Der Mee
,
M. Z. Nashed
,
Sebastiano Seatzu
Journal:
Advances in Computational Mathematics  Adv. Comput. Math.
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