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Some transmutation methods for canonical systems

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Differential Equations in Banach Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1223))

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References

  1. V. Adamyan, On the theory of canonical differential operators in Hilbert space, DAN SSSR, 178 (1968), 9–12

    MathSciNet  Google Scholar 

  2. Z. Agranovič and V. Marčenko, The inverse problem of scattering theory, Gordon-Breach, N.Y., 1963

    Google Scholar 

  3. D. Alpay and H. Dym, Hilbert spaces of analytic functions, inverse scattering, and operator models, I, Integ. Eqs. Oper. Theory, 7 (1984), 589–641

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Alpay and H. Dym, Hilbert spaces of analytic functions, inverse scattering, and operator models, II, Integ. Eqs. Oper. Theory, 8 (1985), 145–180

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Carroll, Transmutation, scattering theory, and special functions, North-Holland, Amsterdam, 1982

    MATH  Google Scholar 

  6. R. Carroll, Transmutation theory and applications, North-Holland, Amsterdam, 1985, to appear

    MATH  Google Scholar 

  7. R. Carroll, Patterns and structure in systems governed by linear second order differential equations, Acta Applicandae Math., to appear

    Google Scholar 

  8. R. Carroll and S. Dolzycki, Transmutation for systems and transmission lines, to appear

    Google Scholar 

  9. Yu. Daletskij and M. Krein, Stability of solutions of differential equations in Banach space, AMS Translations, Vol. 43, 1974

    Google Scholar 

  10. L. deBranges, Hilbert spaces of entire functions, Prentice-Hall, 1968

    Google Scholar 

  11. H. Dym and A. Iacob, Positive definite extensions, canonical equations, and inverse scattering, Topics in Operator Theory, Birkhauser, Basel, 1984, pp. 141–240

    MATH  Google Scholar 

  12. I. Gokhberg and M. Krein, The theory of Volterra operators in Hilbert space and applications, Moscow, 1967

    Google Scholar 

  13. T. Kailath, RKHS approach to detection and estimation problems, I, IEEE Trans. IT-17 (1971), 530–549

    MathSciNet  MATH  Google Scholar 

  14. T. Kailath, R. Geesey, and H. Weinert, Some relations among RKHS norms, Fredholm equations, and innovations representations, IEEE Trans. IT-18 (1972), 341–348

    MathSciNet  MATH  Google Scholar 

  15. T. Kailath and D. Duttweiler, RKHS approach to detection and estimation problems, III, IV, and V, IEEE Trans. IT-18 (1972), 730–745; IT-19 (1973), 19–28 and 29–37

    MathSciNet  MATH  Google Scholar 

  16. T. Kailath and H. Weinert, RKHS approach to detection and estimation problems, II, IEEE Trans. IT-21 (1975), 15–23

    MathSciNet  MATH  Google Scholar 

  17. P. Lax and R. Phillips, Scattering theory and automorphic functions, Bull. Amer. Math. Soc., 2 (1980), 261–295

    Article  MathSciNet  MATH  Google Scholar 

  18. B. Levitan, Inverse Sturm-Liouville problems, Moscow, 1984

    Google Scholar 

  19. B. Levitan and I. Sargsyan, Introduction to spectral theory ..., Moscow, 1970

    Google Scholar 

  20. J. Loeffel, On an inverse problem in potential scattering theory, Annal. Inst. H. Poincaré, 8 (1968), 339–447

    MathSciNet  MATH  Google Scholar 

  21. V. Marčenko, Sturm-Liouville operators and their applications, Kiev, 1977

    Google Scholar 

  22. F. Melik-Adamyan, On canonical differential operators in Hilbert space, Izves. Akad. Nauk Armen. SSR, 12 (1977), 10–31

    MathSciNet  MATH  Google Scholar 

  23. P. Melik-Adamyan, On scattering theory for canonical differential operators, Izves. Akad. Nauk Armen. SSR, 11 (1976), 291–313

    MATH  Google Scholar 

  24. R. Carroll, Transmutation and operator differential equations, North-Holland, Amsterdam, 1979

    MATH  Google Scholar 

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Angelo Favini Enrico Obrecht

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© 1986 Springer-Verlag

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Carroll, R. (1986). Some transmutation methods for canonical systems. In: Favini, A., Obrecht, E. (eds) Differential Equations in Banach Spaces. Lecture Notes in Mathematics, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099180

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  • DOI: https://doi.org/10.1007/BFb0099180

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17191-1

  • Online ISBN: 978-3-540-47350-3

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