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  • 1990-1994  (1)
  • 1980-1984  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    On an extension problem, generalized fourier analysis, and an entropy formula (1980)
    Springer
    Integral equations and operator theory 3 (1980), S. 143-215 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let h(t) be an n × n matrix valued function on the interval |t| ⩽ τ with summable entries. Let ĥ denote the Fourier transform of h and let e denote the n × n identity matrix. Necessary and sufficient conditions for the existence of an extension u of h to the full line such that e-û admits either a left or a right canonical factorization and the inverse transform of (e-û)−1-e vanishes for |t| ⩾ τ are presented and discussed. The connections between these extensions and a generalized Fourier transform are then explored in detail with the help of the theory of triangular factorization. It is then shown that if an allied finite Wiener-Hopf operator based on h is positive, then h admits exactly one extension of the type alluded to above. This extension is then characterized in terms of an entropy integral.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01682992
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Factorization and the Schur-Cohn matrix of a matrix polynomial (1992)
    Springer
    Integral equations and operator theory 15 (1992), S. 1-15 
    Details
    ISSN: 1420-8989
    Keywords: Primary 12D10 ; Secondary 15A22 ; 47A56 ; 93B55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193763
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On unitary interpolants and Fredholm infinite block Toeplitz matrices (1983)
    Springer
    Integral equations and operator theory 6 (1983), S. 863-878 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Conditions for the existence and uniqueness of unitary n × n matrix valued functions f on the unit circle with prescribed Fourier coefficients fj for j ⩾ 0 are given (in terms of infinite block Hankel matrices based on the prescribed coefficients f0,f1,⋯ ) for a natural class of functions. A unitary function belongs to this class if and only if it admits a generalized factorization (in a sense which will be made precise in the paper) or equivalently if and only if any one (and hence both) of the two Toeplitz operators defined by the function are Fredholm. In particular this class includes all continuous unitary n × n matrix valued functions. It is shown that the nonnegative factorization indices of every such unitary f are uniquely determined by f0,f1,⋯ and formulas for them are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01691928
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Hilbert spaces of analytic functions, inverse scattering and operator models.I (1984)
    Springer
    Integral equations and operator theory 7 (1984), S. 589-641 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops a method for obtaining linear fractional representations of a givenn×n matrix valued function which is analytic and contractive in either the unit disc or the open upper half plane. The method depends upon the theory of reproducing kernel Hilbert spaces of vector valued functions developed by de Branges. A self-contained account of the relevant aspects of these spaces to this study is included. In addition, the methods alluded to above are used in conjunction with some ideas of Krein, to develop models for simple, closed symmetric [resp. isometric] operators with equal deficiency indices. A number of related issues and applications are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195919
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    4.6. Span of trigonometric sums in weighted L2 spaces (1984)
    Springer
    Journal of mathematical sciences 26 (1984), S. 2216-2217 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221544
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    Paper (German National Licenses)
    Fulltext
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