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M(λ)-computation for singular differential systems

  • Hans G. Kaper (a1) and Allan M. Krall (a2)

Synopsis

Depending upon the initial data associated with the fundamental matrix, the function M(λ), used to generate L2-solutions of homogeneous linear differential systems, may vary. We show that there is a matrix bilinear transformation between such functions M(λ) with different initial data and illustrate how the result can be used to simplify the calculation of a specific M(λ)-function for a scalar second-order problem.

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1Bennewitz, C.. A note on the Titchmarsh-Weyl m-function. In Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems, ANL-87-26, Vol. 2, pp. 105111 (Argonne, IL; Argonne National Laboratory, 1988).
2Everitt, W. N. and Bennewitz, C.. Some remarks on the Titchmarsh-Weyl m(λ)-coefficient. In Tribute to Ake Pleijel (Uppsala: Department of Mathematics, University of Uppsala, 1980).
3Hinton, D. B. and Shaw, J. K.. Titchmarsh's λ-dependent Boundary Conditions for Hamiltonian Systems, Lecture No tes in Math. 964, pp. 298317 (Berlin: Springer, 1982).
4Kaper, H. G. and Kwong, M. K.. Asymptotics of the Titchmarsh–Weyl m-coefficient for integrable potentials. Proc. Roy. Soc. Edinburgh Sec. A 103 (1986), 347358.
5Kaper, H. G. and Kwong, M. K.. Asymptotics of the Titchmarsh-Weyl m-coefficient for Integrable Potentials II, Lecture Notes in Math. 1285, pp. 222229 (Berlin: Springer, 1987).

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