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1. CMB 2011 (vol 54 pp. 506)
| On the Canonical Solution of the Sturm-Liouville Problem with Singularity and Turning Point of Even Order |
| On the Canonical Solution of the Sturm-Liouville Problem with Singularity and Turning Point of Even Order In this paper, we are going to investigate the canonical property of solutions of
systems of differential equations having a singularity and turning
point of even order. First, by a replacement, we transform the system
to the Sturm-Liouville equation with turning point. Using of the
asymptotic estimates provided by Eberhard, Freiling, and Schneider
for a special fundamental system of solutions of the Sturm-Liouville
equation, we study the infinite product representation of solutions of the systems. Then we
transform the Sturm-Liouville equation with
turning point to the
equation with singularity, then we study the asymptotic behavior of its solutions. Such
representations are relevant to the inverse spectral problem.
Keywords:turning point, singularity, Sturm-Liouville, infinite products, Hadamard's theorem, eigenvalues Categories:34B05, 34Lxx, 47E05 |

