scholarly journals Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Maria Charina ◽  
Vladimir Yu. Protasov
Keyword(s):  
Analytic Functions ◽  
Finitely Generated ◽  
Subdivision Schemes ◽  
Exponential Polynomials ◽  
Compactly Supported ◽  
Shift Invariant Spaces ◽  
Local Shift ◽  
Invariant Spaces

AbstractIn this paper we characterize all subspaces of analytic functions in finitely generated shift-invariant spaces with compactly supported generators and provide explicit descriptions of their elements. We illustrate the differences between our characterizations and Strang-Fix or zero conditions on several examples. Consequently, we depict the analytic functions generated by scalar or vector subdivision with masks of bounded and unbounded support. In particular, we prove that exponential polynomials are indeed the only analytic limits of level dependent scalar subdivision schemes with finitely supported masks.

scholarly journals Moment computation in shift invariant spaces

1998 ◽  
Vol 11 (4) ◽  
pp. 465-479
Author(s):  
David A. Eubanks ◽  
Patrick J. van Fleet ◽  
Jianzhong Wang
Keyword(s):  
Error Estimate ◽  
Rate Of Convergence ◽  
Invariant Space ◽  
Finitely Generated ◽  
Inner Products ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Shift Invariant Space

An algorithm is given for the computation of moments of f∈S, where S is either a principal h-shift invariant space or S is a finitely generated h-shift 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 inner products in these spaces. As corollaries, we derive Marsden-type identities for principal h-shift invariant spaces and finitely generated h-shift invariant spaces. Applications to wavelet/multiwavelet spaces are presented.

Reconstruction from convolution random sampling in local shift invariant spaces

2019 ◽  
Vol 35 (12) ◽  
pp. 125008 ◽  
Author(s):  
Yaxu Li ◽  
Jinming Wen ◽  
Jun Xian
Keyword(s):  
Random Sampling ◽  
Shift Invariant Spaces ◽  
Local Shift ◽  
Invariant Spaces

scholarly journals Construction of Frames for Shift-Invariant Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Stevan Pilipović ◽  
Suzana Simić
Keyword(s):  
Invariant Subspace ◽  
Riesz Basis ◽  
Fourier Transforms ◽  
Weighted Shift ◽  
Invariant Space ◽  
Compactly Supported ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Shift Invariant Space

We construct a sequence{ϕi(·-j)∣j∈ℤ,  i=1,…,r}which constitutes ap-frame for the weighted shift-invariant spaceVμp(Φ)={∑i=1r∑j∈ℤci(j)ϕi(·-j)∣{ci(j)}j∈ℤ∈ℓμp,  i=1,…,r},p∈[1,∞], and generates a closed shift-invariant subspace ofLμp(ℝ). The first construction is obtained by choosing functionsϕi,i=1,…,r, with compactly supported Fourier transformsϕ^i,i=1,…,r. The second construction, with compactly supportedϕi,i=1,…,r,gives the Riesz basis.

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