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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 88, Issue 3-4
  • January 1981, pp. 345-356

On the location of the Weyl circles

  • F. V. Atkinson (a1)
  • DOI:
  • Published online: 14 November 2011

The paper deals with explicit estimates concerning certain circles in the complex plane which were associated with Sturm–Liouville problems by H. Weyl. By the use of Riccati equations instead of linear integral equations, improvements are obtained for results of Everitt and Halvorsen concerning the behaviour of the Titchmarsh–Weyl m-coefficient.

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2E. Brändas and M. Hehenberger . Determination of Weyl's m-cofficient for a continuous spectrum. In Ordinary and Partial Differential Equations, pp. 316322, Proceedings of the Conference held at Dundee, Scotland, March 26–29, 1974 Lecture Notes in Mathematics 415 (Berlin: Springer, 1974).

5W. N. Everitt and S. G. Halvorsen . On the asymptotic form of the Titchmarsh–Weyl m-coefficient. Applicable Anal. 8 (1978), 153169.

6C. Fulton . Parametrizations of Titchmarsh's m(λ)-functions in the limit-circle case. Trans. Amer. Math. Soc. 229 (1977), 5163 (also Ph.D. Dissertation, Rhein-Westf. Technische Hochschule, Aachen, 1973).

8H. Weyl . Ueber gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann. 68 (1910), 220269.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
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