English

Regularization of binomial differential equations with singular coefficients

Functional Analysis 2012-02-21 v1

Abstract

We propose a regularization of the formal differential expression of order m3m \geqslant 3 l(y)=imy(m)(t)+q(t)y(t),t(a,b), l(y) = i^my^{(m)}(t) + q(t)y(t), \,t \in (a, b), applying quasi-derivatives. The distribution coefficient qq is supposed to have an antiderivative QL([a,b];C)Q \in L([a,b];\mathbb{C}). For the symmetric case (Q=QˉQ = \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=2m = 2 for QL2([a,b];C)Q \in L_2([a, b];\mathbb{C}) was investigated earlier.

Keywords

Cite

@article{arxiv.1106.3275,
  title  = {Regularization of binomial differential equations with singular coefficients},
  author = {Andrii Goriunov and Vladimir Mikhailets},
  journal= {arXiv preprint arXiv:1106.3275},
  year   = {2012}
}

Comments

In Russian, 14 pages

R2 v1 2026-06-21T18:23:27.453Z