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  • 30E05  (5)
  • Primary 47A57  (2)
  • Secondary 30E05  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    J-inner matrix functions, interpolation and inverse problems for canonical systems, I: Foundations (1997)
    Springer
    Integral equations and operator theory 29 (1997), S. 373-454 
    Details
    ISSN: 1420-8989
    Keywords: 30E05 ; 30D99 ; 34A55 ; 34L30 ; 47A56 ; 47A57
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This is the first of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted largely to foundational material (much of which is of independent interest) on the theory of assorted classes of meromorphic matrix valued functions. Particular attention is paid to the structure of J-inner functions and connections with bitangential interpolation problems and reproducing kernel Hilbert spaces. Some new characterizations of regular, singular and strongly regular J-inner functions in terms of the associated reproducing kernel Hilbert spaces are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193811
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    J-Inner matrix functions, interpolation and inverse problems for canonical systems, II: The inverse monodromy problem (2000)
    Springer
    Integral equations and operator theory 36 (2000), S. 11-70 
    Details
    ISSN: 1420-8989
    Keywords: 30E05 ; 30D99 ; 34A55 ; 34L40 ; 47A56 ; 47A57
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This is the second of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted to the inverse monodromy problem for canonical integral and differential systems. In this part, which focuses on the case of a diagonal signature matrixJ, a parametrization is obtained of the set of all solutionsM (t) for the inverse problem for integral systems in terms of two chains of entire matrix valued inner functions. Special classes of solutions correspond to special choices of these chains. This theme will be elaborated upon further in a third part of this paper which will be published in a subsequent issue of this journal. There the emphasis will be on symmetries and growth conditions all of which serve to specify or restrict the chains alluded to above, from the outside, so to speak.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01236286
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    J-inner matrix functions, interpolation and inverse problems for canonical systems, III: More on the inverse monodromy problem (2000)
    Springer
    Integral equations and operator theory 36 (2000), S. 127-181 
    Details
    ISSN: 1420-8989
    Keywords: 30E05 ; 30D99 ; 34A55 ; 34L40 ; 47A56 ; 47A57
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is a continuation of our study of the inverse monodromy problem for canonical systems of integral and differential equations which appeared in a recent issue of this journal. That paper established a parametrization of the set of all solutions to the inverse monodromy for canonical integral systems in terms of two continuous chains of matrix valued inner functions in the special case that the monodromy matrix was strongly regular (and the signature matrixJ was not definite). The correspondence between the chains and the solutions of this monodromy problem is one to one and onto. In this paper we study the solutions of this inverse problem for several different classes of chains which are specified by imposing assorted growth conditions and symmetries on the monodromy matrix and/or the matrizant (i.e., the fundamental solution) of the underlying equation. These external conditions serve to either fix or limit the class of admissible chains without computing them explicitly. This is useful because typically the chains are not easily accessible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202092
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    More on maximum entropy interpolants and maximum determinant completions of associated Pick matrices (1996)
    Springer
    Integral equations and operator theory 24 (1996), S. 188-229 
    Details
    ISSN: 1420-8989
    Keywords: Primary 47A57 ; Secondary 30E05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01193460
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    On three Krein extension problems and some generalizations (1998)
    Springer
    Integral equations and operator theory 31 (1998), S. 1-91 
    Details
    ISSN: 1420-8989
    Keywords: 30E05 ; 42A82 ; 47A56 ; 47A57
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Three basic extension problems which were initiated by M. G. Krein are discussed and further developed. Connections with interpolation problems in the Carathéodory class are explained. Some tangential and bitangential versions are considered. Full characterizations of the classes of resolvent matrices for these problems are given and formulas for the resolvent matrices of left tangential problems are obtained using reproducing kernel Hilbert space methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01203457
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    On maximum entropy interpolants and maximum determinant completions of associated Pick matrices (1995)
    Springer
    Integral equations and operator theory 23 (1995), S. 61-88 
    Details
    ISSN: 1420-8989
    Keywords: Primary 47A57 ; Secondary 30E05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we shall show that “the value” of the maximum ω-entropy solution of an interpolation problem of the Nevanlinna-Pick type at the point ω maximizes the determinant of the solution of an associated matrix completion problem. This serves to show that the solutions of two distinct extremal problems coincide.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261203
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    On degenerate interpolation, entropy and extremal problems for matrix Schur functions (1998)
    Springer
    Integral equations and operator theory 32 (1998), S. 367-435 
    Details
    ISSN: 1420-8989
    Keywords: 47A57 ; 30E05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a general bitangential interpolation problem for matrix Schur functions and focus mainly on the case when the associated Pick matrix is singular (and positive semidefinite). Descriptions of the set of all solutions are given in terms of special linear fractional transformations which are obtained using two quite different approaches. As applications of the obtained results we consider the maximum entropy and the maximum determinant extension problems suitably adapted to the degenerate situation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194989
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    Paper (German National Licenses)
    Fulltext
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