I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2006, VOLUME 12, NUMBER 6, PAGES 231-239
Birkhoff regularity in terms of the growth of the norm for the Green
E. A. Shiryaev
View as HTML
View as gif image
We consider the ordinary differential operator generated on by the differential
and linearly independent
homogeneous boundary conditions at the endpoints.
We assume that the coefficients are
Lebesgue integrable complex functions.
If the boundary conditions are Birkhoff regular, then the Green
function , being the kernel
of the operator ,
admits the asymptotic estimate (for sufficiently large )
a certain constant.
In the present paper, we prove the converse assertion: the fulfillment
of this estimate on some rays implies the regularity of the
Last modified: February 26, 2007