On the asymptotic form of the Titchmarsh-Weyl m-coefficient†

†Dedicated to the memory of Arthur Endélyi on the occasion of his seventieth birthday

Abstract

The asymptotic form of the Titchmarsh-Weyl m-coefficient for the differential equation −(py′)′+q j = λwy on [a, b). (′≡d/dx), as |λ|→∞, is obtained under general conditions on the real-valued coefficients p, q and w, with p≧0 and w≧0. Examples are given to show that the result is near to but possible, although there are many interesting cases for which the asymptotic form of the m-coefficient is still not known.

†Dedicated to the memory of Arthur Endélyi on the occasion of his seventieth birthday

†Dedicated to the memory of Arthur Endélyi on the occasion of his seventieth birthday

Notes

†Dedicated to the memory of Arthur Endélyi on the occasion of his seventieth birthday

Additional information

Notes on contributors

W. N. Everitt

S. G. Halvorsen