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  • 1
    Book
    Book
    ¬An¬ introduction to Wavelets (1992)
    London u.a. :Academic Press,
    Details
    Title: ¬An¬ introduction to Wavelets
    Author: Chui, Charles K.
    Publisher: London u.a. :Academic Press,
    Year of publication: 1992
    Pages: 266 S.
    Series Statement: Wavelets analysis and its applications
    Type of Medium: Book
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  • 2
    Book
    Book
    Wavelets: a tutorial in theory and applications (1992)
    London u.a. :Academic Press,
    Details
    Title: Wavelets: a tutorial in theory and applications
    Contributer: Chui, Charles K.
    Publisher: London u.a. :Academic Press,
    Year of publication: 1992
    Pages: 729 S.
    Series Statement: Wavelets analysis and its applications
    Type of Medium: Book
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  • 3
    Electronic Resource
    Electronic Resource
    High-Order Orthonormal Scaling Functions and Wavelets Give Poor Time-Frequency Localization (1995)
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 415-426 
    Details
    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the time-frequency windows tend to infinity as n → ∞. This class includes those of Battle-Lemarie and Daubechies. In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s00041-001-4035-2
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A general study of maximal robust stability regions (1991)
    Springer
    Circuits, systems and signal processing 10 (1991), S. 15-30 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In the study of robust stability, the largest coefficient region of a given stable polynomial that guarantees stability preservation under perturbation of coefficients is to be determined. A general consideration including both Hurwitz and Schur polynomials is treated in this paper. For this purpose, the notion ofperturbation constant is introduced. As a consequence of our results, we also introduce a general Kharitonov-type stability test which is based on testing the stability and perturbation constant of a single polynomial.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183238
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Rate of convergence of schmidt pairs and rational functions corresponding to best approximants of truncated hankel operators (1992)
    Springer
    Mathematics of control, signals, and systems 5 (1992), S. 67-79 
    Details
    ISSN: 1435-568X
    Keywords: Hankel norm ; Rational approximation ; Order of approximation ; Wiener class
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract The problem of approximating Hankel operators of infinite rank by finite-rank Hankel operators is considered. For efficiency, truncated infinite Hankel matrices Γn of Γ are utilized. In this paper for any compact Hankel operator Γ of the Wiener class, we derive the rate of l2-convergence of the Schmidt pairs of Γn to the corresponding Schmidt pairs of Γ. For a certain subclass of Hankel operators of the Wiener class, we also obtain the rate of l1-convergence. In addition, an upper bound for the rate of uniform convergence of the rational symbols of best rank-k Hankel approximants of Γn to the corresponding rational symbol of the best rank-k Hankel approximant to Γ asn → ∞ is derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211976
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Convergence of certain quadrature processes (1972)
    Springer
    Aequationes mathematicae 8 (1972), S. 318-318 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01844517
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    A General framework for local interpolation (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 569-581 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 41A15 ; 65D05 ; CR: G1.1
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a general framework for the construction of local interpolation methods with a given approximation order. Some applications to multivariate spline spaces are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385640
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  • 9
    Electronic Resource
    Electronic Resource
    A characterization of multivariate quasi-interpolation formulas and its applications (1990)
    Springer
    Numerische Mathematik 57 (1990), S. 105-121 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 41A15, 41A25, 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Let ϕ be a compactly supported function on ℝ s andS (ϕ) the linear space withgenerator ϕ; that is,S (ϕ) is the linear span of the multiinteger translates of ϕ. It is well known that corresponding to a generator ϕ there are infinitely many quasi-interpolation formulas. A characterization of these formulas is presented which allows for their direct calculation in a variety of forms suitable to particular applications, and in addition, provides a clear formulation of the difficult problem of minimally supported quasi-interpolants. We introduce a generalization of interpolation called μ-interpolation and a notion of higher order quasi-interpolation called μ-approximation. A characterization of μ-approximants similar to that of quasi-interpolants is obtained with similar applications. Among these applications are estimating least-squares approximants without matrix inversion, surface fitting to incomplete or semi-scattered discrete data, and constructing generators with one-point quasi-interpolation formulas. It will be seen that the exact values of the generator ϕ at the multi-integers ℤ s facilitates the above study. An algorithm to yield this information for box splines is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386401
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Approximation with restricted spectra (1975)
    Springer
    Mathematische Zeitschrift 144 (1975), S. 289-297 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214143
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