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  • 42C15 (primary)  (1)
  • Approximation order  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Affine frames, quasi-affine frames, and their duals (1998)
    Springer
    Advances in computational mathematics 8 (1998), S. 1-17 
    Details
    ISSN: 1572-9044
    Keywords: affine frame ; quasi-affine frame ; dual ; sesquilinear operator ; translation invariance ; 42C15 (primary) ; 42B15 ; 47N40 (secondary)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The notion of quasi-affine frame was recently introduced by Ron and Shen [9] in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we establish a duality-preservation theorem for quasi-affine frames. Furthermore, the preservation of frame bounds when changing an affine frame to a quasi-affine frame is shown to hold without the decay assumptions in [9]. Our consideration leads naturally to the study of certain sesquilinear operators which are defined by two affine systems. The translation-invariance of such operators is characterized in terms of certain intrinsic properties of the two affine systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018975725857
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On bivariate super vertex splines (1990)
    Springer
    Constructive approximation 6 (1990), S. 399-419 
    Details
    ISSN: 1432-0940
    Keywords: Multivariate ; Splines ; Super splines ; Approximation order ; Bézier net ; Interpolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A vertex spline basis of the super-spline subspace $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{S} _d^r : = S_d^{r,r + \left\lfloor {(d - 2r - 1)/2} \right\rfloor } (\Delta )$$ of Sd r(Δ), where d≥3r+2 and Δ is an arbitrary triangulation inR 2, is constructed, so that the full approximation order ofd+1 can be achieved via an approximation formula using this basis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01888272
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    Paper (German National Licenses)
    Fulltext
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