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INVARIANCE OF A SHIFTINVARIANT SPACE
"... Abstract. A shiftinvariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shiftinvariant subspaces S that are also invaria ..."
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Cited by 11 (5 self)
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Abstract. A shiftinvariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those shiftinvariant subspaces S that are also
Shiftinvariant spaces on the real line
 Proc. Amer. Math. Soc
, 1997
"... (Communicated by J. Marshall Ash) Abstract. We investigate the structure of shiftinvariant spaces generated by a finite number of compactly supported functions in Lp(R) (1≤p≤∞). Based on a study of linear independence of the shifts of the generators, we characterize such shiftinvariant spaces in t ..."
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Cited by 35 (7 self)
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(Communicated by J. Marshall Ash) Abstract. We investigate the structure of shiftinvariant spaces generated by a finite number of compactly supported functions in Lp(R) (1≤p≤∞). Based on a study of linear independence of the shifts of the generators, we characterize such shiftinvariant spaces
Moment Computation in Shift Invariant Spaces
"... An algorithm is given for the computation of moments of f 2 S, where S is either a principal hshift invariant space or S is a finitely generated hshift invariant space. An error estimate for the rate of convergence of our scheme is also presented. In so doing, we obtain a result for computing inne ..."
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An algorithm is given for the computation of moments of f 2 S, where S is either a principal hshift invariant space or S is a finitely generated hshift invariant space. An error estimate for the rate of convergence of our scheme is also presented. In so doing, we obtain a result for computing
The spectral function of shiftinvariant spaces
 Michigan Math. J
"... Abstract. We extend the notion of the spectral function of shiftinvariant spaces introduced by the authors in [BRz] to the case of general lattices. The main feature is that the spectral function is not dependent on the choice of the underlying lattice with respect to which a space is shiftinvaria ..."
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Cited by 21 (6 self)
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Abstract. We extend the notion of the spectral function of shiftinvariant spaces introduced by the authors in [BRz] to the case of general lattices. The main feature is that the spectral function is not dependent on the choice of the underlying lattice with respect to which a space is shiftinvariant
Shiftinvariant spaces and linear operator equations
 Israel J. Math
, 1998
"... In this paper we investigate the structure of finitely generated shiftinvariant spaces and solvability of linear operator equations. Fourier transforms and semiconvolutions are used to characterize shiftinvariant spaces. Criteria are provided for solvability of linear operator equations, includin ..."
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Cited by 47 (10 self)
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In this paper we investigate the structure of finitely generated shiftinvariant spaces and solvability of linear operator equations. Fourier transforms and semiconvolutions are used to characterize shiftinvariant spaces. Criteria are provided for solvability of linear operator equations
Nonuniform Sampling and Reconstruction in ShiftInvariant Spaces
, 2001
"... This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shiftinvariant spaces. It is a survey as well as a research paper and provides a unied framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing together ..."
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Cited by 219 (13 self)
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This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shiftinvariant spaces. It is a survey as well as a research paper and provides a unied framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing
INTERSECTION OF DILATES OF SHIFTINVARIANT SPACES MARCIN BOWNIK
"... Abstract. We prove that if the dimension function of a shiftinvariant space V is not constantly ∞, then the intersection of (negative) dilates of V must be trivial. We also give an example of two refinable shiftinvariant spaces with identical spectral functions such that this intersection is eithe ..."
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Abstract. We prove that if the dimension function of a shiftinvariant space V is not constantly ∞, then the intersection of (negative) dilates of V must be trivial. We also give an example of two refinable shiftinvariant spaces with identical spectral functions such that this intersection
Determining sets of shift invariant spaces
 Proceedings of ICWA (Chenai
, 2003
"... Abstract. The problem of determining an appropriate signal or image model from experimental data is addressed. Specifically, given a finite set of signals or images belonging to a fixed but unknown shift invariant space, the problem is whether the known signals at hand are sufficient for determining ..."
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Cited by 2 (1 self)
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Abstract. The problem of determining an appropriate signal or image model from experimental data is addressed. Specifically, given a finite set of signals or images belonging to a fixed but unknown shift invariant space, the problem is whether the known signals at hand are sufficient
The Structure of Finitely Generated ShiftInvariant Spaces in ...
, 1992
"... : A simple characterization is given of finitely generated subspaces of L 2 (IR d ) which are invariant under translation by any (multi)integer, and used to give conditions under which such a space has a particularly nice generating set, namely a basis, and, more than that, a basis with desirable ..."
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Cited by 160 (20 self)
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properties, such as stability, orthogonality, or linear independence. The last property makes sense only for `local' spaces, i.e., shiftinvariant spaces generated by finitely many compactly supported functions, and special attention is paid to such spaces. As an application, we prove
QuasiInterpolation in Shift Invariant Spaces
, 2000
"... Let s # 1 be an integer, # : R s # R be a compactly supported function, and S(#) denote the linear span of {#(  k) : k # Z s }. We consider the problem of approximating a continuous function f : R s # R on compact subsets of R s from the classes S(#(h)), h > 0, based on samples ..."
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Cited by 4 (2 self)
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on samples of the function at scattered sites in R s . We demonstrate how classical polynomial inequalities lead to the construction of local, quasiinterpolatory operators for this purpose. 1 Introduction An important subject in approximation theory is the study of shiftinvariant spaces generated by a
Results 1  10
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