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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Advances in computational mathematics 8 (1998), S. 1-17 
    ISSN: 1572-9044
    Schlagwort(e): affine frame ; quasi-affine frame ; dual ; sesquilinear operator ; translation invariance ; 42C15 (primary) ; 42B15 ; 47N40 (secondary)
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Constructive approximation 1 (1985), S. 121-135 
    ISSN: 1432-0940
    Schlagwort(e): 41 A 20 ; 30 E 10 ; Order of approximation ; Rational functions and electrostatic fields due to distribution of electrons ; Bers space ; Jordan domain ; Conformal mapping
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract LetD be a Jordan domain in the complex plane andA q (D) the Bers space with norm ∥ ∥ q . IfD is the unit disk, it is known that ∥S n 0∥2≥π/18, whereS n =∑ k=1 n l/(z−z nk ) withz nk ∈∂D, so that approximation in ∥ ∥ q ,q〈-2, is not possible. In this paper, we give an order of estimate of ∥f−S n ∥ q for 2〈q〈∞ when ∂D is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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