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  • 1975-1979  (3)
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Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Trace formulas for pair operators (1978)
    Springer
    Integral equations and operator theory 1 (1978), S. 152-175 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we shall study the Fredholm determinant and related trace formulas for a class of operators which correspond to the restriction of integral operators with kernels of the form k(x,y) = χ(x)gv(x−y)+[1−χ(x)]fv(x−y) to the square |x|,|y| ⩽ T and shall evaluate the limit as T ↑ ∞ . Here χ denotes the indicator function of the right half-line [0,∞) . The results obtained generalize the well known formulas of M. Kac for the classical convolution operator in which g = f .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01690981
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the inverse spectral problem for the string equation (1978)
    Springer
    Integral equations and operator theory 1 (1978), S. 270-277 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The theory of Hilbert spaces of entire functions is used to deduce the changes in the mass distribution of a string effected by a small change in its spectral function. The formula of Gelfand-Levitan emerges as a special case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01690986
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Extensions of matrix valued functions with rational polynomial inverses (1979)
    Springer
    Integral equations and operator theory 2 (1979), S. 503-528 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let Rj : |j| ⩽ m, be a given set of n×n matrices. Necessary and sufficient conditions for the existence and uniqueness of an invertible function F(ζ) = Σ Fjζj in the Wiener algebra of n×n matrix valued functions on the unit circle |ζ| = 1 such that Fj=Rj for |j| ⩽ m, and F admits either a right or a left canonical factorization and the matrix Fourier coefficients of F−1 vanish for |j| 〉 m are presented and discussed. In the special case that the block Toeplitz matrix based on the given Rj is positive definite there is exactly one such extension: the so-called maximum entropy or autoregressive extension of statistical estimation theory. Some special properties of this extension are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01691075
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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