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Topics in Interpolation Theory of Rational Matrix-Valued Functions

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Topics in Interpolation Theory of Rational Matrix-Valued Functions
  • Forlagets pris kr. 1.039,95
  • Leveringstid 5-9 hverdage
  • Forventet levering 01-08-2018
  • Bog, hæftet (kr. 694,95) (kr. 694,95)
    1. Beskrivelse

      One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.

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    2. Yderligere info
      Udgivelsesdato:
      01-08-2014
      Sprog:
      Engelsk
      ISBN13:
      9783034854719
      Sidetal:
      260
      Vægt:
      422 g
      Højde:
      14 mm
      Bredde:
      170 mm
      Længde:
      244 mm
      Forlag:
      Birkhäuser
      Mærkat:
      Bog, hæftet
      Format:
      Hæftet
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