Some Remarks on a Canonical Marcenko Equation

References

• Carroll , R. 1983 . On the connection of differential operators via scattering input . CR Royal Soc. Canada , 5 : 87 – 90 .
   Google Scholar
• Carroll , R. 1984 . “ Some topics in transmutation ” . In Differential Equations , 87 – 104 . North-Holland : Math. Studies 92 .
   Google Scholar
• Carroll R Patterns and structure in systems governed by linear second order differential equations Acta Applic. Math to appear
   Google Scholar
• Carroll , R. 1982 . The Gelfand-Levitan and Marčenko equation via transmutation . Rocky Mount. Jour. Math. , 12 : 393 – 427 .
   Web of Science ®Google Scholar
• Carroll , R. 1982 . Transmutation, scattering theory, and special functions North-Holland
   Google Scholar
• Carroll , R. and CarroTl , R. 1984 . Least squares, transmutation, and the Marčenko equation . CR Royal Soc. Canada , 6 : 85 – 88 .
   Google Scholar
• Carroll R The Marcenko equation as a minimizing criterion to appear
   Google Scholar
• Carroll R Transmutation via the momentum plane Math. Meth. Appl. Sci to appear
   Google Scholar
• Carroll , R. 1983 . Transmutation theory for certain radial operators . Proc. Japan Acad. , 59 : 51 – 54 .
   Google Scholar
• Carroll , R. and Dolzycki , S. 1984 . Transmutation as a minimizina procedure . Jour. Math. Physics , 25 : 91 – 93 .
   Google Scholar
• Carroll , R. and Gilbert , J. 1981 . Remarks on transmutation, scattering theory, and special functions . Math. Annalen , 258 : 39 – 54 .
   Web of Science ®Google Scholar
• Carroll , R. and Santosa , F. 1981 . Scattering techniques for a one dimensional inverse problem in geophysics . Math. Meth. Appl. Sci. , 3 : 145 – 171 .
   Google Scholar
• Carroll , R. and Santosa , F. 1985 . Some transmutation methods in geophysics 230 – 244 . North-Holland
   Google Scholar
• Carroll , R. and Santosa , F. 1984 . Impedance profile recovery from transmission data . Jour. Acous, Soc. Amer. , 76 : 935 – 941 .
   Web of Science ®Google Scholar
• Chadan , K. and Sabatier , P. 1977 . Inverse problems in quantum scattering theory , N.Y. : Springer .
   Google Scholar
• Dym , H. and Iacob , A. 1982 . “ Applications of factorization and Toeplitz operators to inverse problems ” . In Toeplitz Centennial , 233 – 260 . Basel : Birkhauser .
   Google Scholar
• Dym , H. and Iacob , A. 1984 . “ Positive definite extensions, canonical equations, and inverse problems ” . In Topics in Operator Theory , 141 – 240 . Basel : Birkhauser .
   Google Scholar
• Fadeev , L. 1959 . The inverse problem of quantum scattering theory . Uspekhi Mat. Nauk , 14 : 57 – 119 .
   Google Scholar
• Fadeev , L. 1975 . The inverse problem of quantum scattering theory, II . Sov. Probs. Mat. , 31 : 93 – 180 .
   Google Scholar
• Hutson , V. 1965 . On a generalization of the Wiener-Hopf integral equation . Jour. Math. Mech. , 14 : 807 – 819 .
   Google Scholar