Regularization of binomial differential equations with singular coefficients

Details Regularization of binomial differential equations with singular coefficients Regularization of binomial differential equations with singular coefficients

2011-06-16

arxiv.org/abs/1106.3275v1

Ukrainian Math. J., 63 (2011), no.9, 1190-1205

Mathematics

Functional Analysis

In Russian, 14 pages

Scientific paper

We propose a regularization of the formal differential expression of order $m \geqslant 3$ $$ l(y) = i^my^{(m)}(t) + q(t)y(t), \,t \in (a, b), $$ applying quasi-derivatives. The distribution coefficient $q$ is supposed to have an antiderivative $Q \in L([a,b];\mathbb{C})$. For the symmetric case ($Q = \bar{Q}$) self-adjoint and maximal dissipative extensions of the minimal operator and its generalized resolvents are described. The resolvent approximation with resrect to the norm of the considered operators is also investigated. The case $m = 2$ for $Q \in L_2([a, b];\mathbb{C})$ was investigated earlier.

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