On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line
Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 416-421
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For the perturbed Hill’s equation on the line, we study the behaviour of the matrix m-function at the spectral gap endpoints. In particular, we extend the result of Hinton, Klaus and Shaw that En , a gap endpoint, is a half-bound state (HBS) if and only if (E − En)1⁄2m(E) approaches a nonzero constant as E → En , to the present case.
Clemence, Dominic P. On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line. Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 416-421. doi: 10.4153/CMB-1997-049-x
@article{10_4153_CMB_1997_049_x,
author = {Clemence, Dominic P.},
title = {On the {Singular} {Behaviour} of the {Titchmarsh-Weyl} {m-Function} for the {Perturbed} {Hill{\textquoteright}s} {Equation} on the {Line}},
journal = {Canadian mathematical bulletin},
pages = {416--421},
year = {1997},
volume = {40},
number = {4},
doi = {10.4153/CMB-1997-049-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-049-x/}
}
TY - JOUR AU - Clemence, Dominic P. TI - On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line JO - Canadian mathematical bulletin PY - 1997 SP - 416 EP - 421 VL - 40 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-049-x/ DO - 10.4153/CMB-1997-049-x ID - 10_4153_CMB_1997_049_x ER -
%0 Journal Article %A Clemence, Dominic P. %T On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line %J Canadian mathematical bulletin %D 1997 %P 416-421 %V 40 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-049-x/ %R 10.4153/CMB-1997-049-x %F 10_4153_CMB_1997_049_x
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