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Original Articles

On symmetric factorizations of rational matrix functions

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Pages 243-261 | Received 10 Aug 1990, Published online: 30 May 2007

References

  • Bart , H. , Gohberg , I. and Kaashoek , M. A. 1979 . Minimal Factorization of Matrix and Operator Functions , Basel : Birkhäuser . OT 1
  • Ball , J. A. , Gohberg , I. and Rodman , L. 1987 . Minimal factorization of meromorphic matrix functions in terms of local data . Integral Equations and Operator Theory , 10 : 309 – 348 .
  • Ball , J. A. , Gohberg , I. and Rodman , L. 1990 . “ Interpolation Problems for Matrix Valued Functions ” . Basel : Birkhäuser . OT 45
  • Ball , J. A. and Helton , J. W. 1984 . Beurling-Lax representations using classical Lie groups with many applications II: GL(n,∈) and Wiener-Hopf factorization . Integral Equations and Operator Theory , 7 : 291 – 309 .
  • Ball , J. A. 1987 . Local inverse spectral problems for rational matrix functions . Integral Equations and Operator Theory , 10 : 349 – 415 .
  • Clements , D. J. and Glover , K. 1989 . Spectral factorizations via hermitian pencils . Linear Algebra and its Applications , 122/123/124 : 797 – 846 .
  • Coppel , W. A. 1972 . Linear Systems. Notes in Pure Mathematics , Vol. 6 , Canberra : Australian National University .
  • Gohberg , I. , Kaashoek , M. A. and Ran , A. C. M. 1988 . “ Interpolation problems for rational matrix functions with incomplete data and Wiener-Hopf factorization ” . In Topics in Interpolation Theory of Rational Matrix Valued Functions , Edited by: Gohberg , I. Basel : Birkhäuser . OT 33
  • Gohberg , I. , Lancaster , P. and Rodman , L. 1982 . Factorization of selfadjoint matrix polynomials with constant signature . Linear and Multilinear Algebra , 11 : 209 – 214 .
  • Gohberg , I. , Lancaster , P. and Rodman , L. 1986 . Invariant Subspaces of Matrices and Applications , New York : John Wiley & Sons .
  • Gohberg , I. , Lancaster , P. and Rodman , L. 1986 . Matrices and Indefinite Scalar Products , Basel : Birkhäuser . OT 8
  • Gohberg , I. , Lancaster , P. and Rodman , L. 1982 . Matrix Polynomials , New York : Academic Press . etc.
  • Gohberg , I. 1983 . A sign characteristic for selfadjoint meromorphic matrix functions . Applicable Analysis , 16 : 165 – 185 .
  • Jacubovič , V. A. 1970 . Factorization of symmetric matrix polynomials . Soviet Math. Doklady , 11 : 1261 – 1264 .
  • Kaashoek , M. A. and Ran , A. C. M. 1986 . “ Symmetric Wiener-Hopf factorization of selfadjoint rational matrix functions and realization ” . In Constructive Methods of Wiener-Hopf Factorization , Edited by: Gohberg , I. and Kaashoek , M. A. Basel : Birkhäuser . OT 21
  • Kailath , T. 1980 . Linear Systems , Englewood Cliffs, NJ : Prentice Hall, Inc. .
  • Kalman , R. E. , Falb , P. L. and Arbib , M. A. 1969 . Topics in Mathematical System Theory , New York : McGraw-Hill .
  • McMillan , B. 1952 . Introduction to formal realizability theory . Bell System Tech. J. , 31 : 541 – 600 .
  • Nikolaïčuk , A. M. and Spitkovskiï , I. M. 1975 . On the Riemann boundary—value problem with hermitian matrix . Soviet Math. Doklady , 16 : 533 – 536 .
  • Ran , A. C. M. 1982 . Minimal factorization of selfadjoint rational matrix functions . Integral Equations and Operator Theory , 5 : 850 – 869 .
  • Ran , A. C. M. and Rodman , L. 1990 . Stable invariant Lagrangian subspaces: factorization of symmetric rational matrix functions and other applications . Linear Algebra and its Applications , 137/138 : 575 – 620 .
  • Ran , A. C. M. and Rodman , L. 1984 . Stability of invariant maximal semidefinite subspaces I . Linear Algebra and its Applications , 62 : 51 – 86 .
  • Ran , A. C. M. and Rodman , L. Laurent interpolation for rational matrix functions and a local factorization principle . Journ. of Mathematical Analysis and Applications , to apear
  • Ran , A. C. M. and Rodman , L. Local minimal factorizations of rational matrix functions in terms of null and pole data: formulas for factors . Integral Equations and Operator Theory , to apear
  • Ran , A. C. M. and Rodman , L. 1984 . Stability of invariant maximal semidefinite subspaces II. Applications: Selfadjoint rational matrix functions, algebraic Riccati equations . Linear Algebra and its Applications , 63 : 133 – 173 .
  • Rellich , F. 1953 . “ Perturbation theory of eigenvalue problems ” . In Lecture Notes , New York Univ. .
  • Roozemond , L. 1986 . “ Canonical pseudo-spectral factorization and Wiener-Hopf integral equations ” . In Constructive Methods of Wiener-Hopf Factorization , Edited by: Gohberg , I. and Kaashoek , M. A. Basel : Birkhäuser . OT 21
  • Rosenblum , M. and Rovnyak , J. 1985 . Hardy Classes and Operator Theory , New York,Oxford : Oxford University Press, Clarendon Press .

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