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18th International Conference on Operator Theory
June 27 - July 1, 2000
University of the West
Timisoara, Romania

Organizers
Dumitru Gaspar, Traian Ceausu, Aurelian Craciunescu, Aurelian Gheondea, Radu-Nicolae Gologan, Ciprian Pop, Dan Popovici, Nicolae Suciu, Alexandru Terescenco, Dan Timotin, Flavius Turcu

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Estimates for Solutions of the Sturm-Liouville Equation
by
Oleksandr Gomilko
Institute of Hydromechanics, Zhelyabov str. 8/4, Kiev 01057, Ukraine
Coauthors: Vyacheslav Pivovarchik

In present communication new (depending on \mu --> \infty) estimates for solutions of the Sturm-Liouville equation
y''(x)+[\mu2\rho(x)-q(x)]y(x)=0,     x in [0, 1]\leqno (*)
are presented. We consider the case of strictly positive weight function \rho(x) of bounded variation and real-valued function q(x) in L1[0, 1]. The main result lies in the following statement: for arbitrary r > 0 any solution y(x, \mu) of equation (*) being normed in L1[0, 1] admits uniform with respect to \mu: |Im \mu| <= r < \infty estimate in the norm of C[0, 1].

Date received: June 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-55.