Sturm-Liouville operators with complex singular coefficients
We consider on the finite interval the Sturm-Liouville differential expression\[l(y)=-(py')'+qy+i((ry)'+ry')\]with coefficients satisfying conditions: $q = Q',$ $1\Big/\sqrt{|p|},$ $Q\Big/\sqrt{|p|},$ $r\Big/\sqrt{|p|} \in L_2,$ where the derivative of fu...
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| Date: | 2017 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2017
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/314 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | We consider on the finite interval the Sturm-Liouville differential expression\[l(y)=-(py')'+qy+i((ry)'+ry')\]with coefficients satisfying conditions: $q = Q',$ $1\Big/\sqrt{|p|},$ $Q\Big/\sqrt{|p|},$ $r\Big/\sqrt{|p|} \in L_2,$ where the derivative of function $Q$ is understood in the sense of distributions. Corresponding operators are correctly defined as quasi-differential. Conditions for the minimal operator to be symmetric are obtained and all its self-adjoint, maximal dissipative and maximal accumulative extensions are described in terms of boundary conditions. |
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