Regularization of two-term differential equations with singular coefficients by quasiderivatives
We propose a regularization of the formal differential expression $$l(y) = i^m y^{(m)}(t) + q(t)y(t),\; t \in (a, b),$$ of order $m \geq 3$ by using quasiderivatives. It is assumed that the distribution coefficient $q$ has an antiderivative $Q \in L ([a, b]; \mathbb{C})$. In the symmetric case $(Q...
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| Date: | 2011 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2797 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We propose a regularization of the formal differential expression
$$l(y) = i^m y^{(m)}(t) + q(t)y(t),\; t \in (a, b),$$
of order $m \geq 3$ by using quasiderivatives. It is assumed that the distribution coefficient $q$ has an antiderivative $Q \in L ([a, b]; \mathbb{C})$.
In the symmetric case $(Q = \overline{Q})$, we describe self-adjoint and maximal dissipative/accumulative
extensions of the minimal operator and its generalized resolvents. In the general (nonselfadjoint)
case, we establish conditions for the convergence of the resolvents of the considered operators in
norm.
The case where $m = 2$ and $Q \in L_2 ([a, b]; \mathbb{C})$ was studied earlier. |
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