Regularization of two-term differential equations with singular coefficients by quasiderivatives
type: Item
instance of: scholarly article
title: Regularization of two-term differential equations with singular coefficients by quasiderivatives
zbMATH Open document ID: 1261.47021
author: A. S. Goryunov
author: Vladimir A. Mikhailets
published in: Ukrainian Mathematical Journal
publication date: 2012-11-23T00:00:00Z
review text: A regularization of the formal differential expression \[ l(y) = i^m y^{(m)}(t) +q(t)y(t) \] under the assumption \(t\in \mathcal{J}:=(a,b)\), \(q = Q^{\prime}\), \(Q\in {L}(\mathcal{J},\mathbb{C})\), is suggested to determine the corresponding maximal and minimal operators in the Hilbert space \({L}_2(\mathcal{J};\mathbb{C})\). Sufficient conditions are established for the uniform resolvent approximation of extensions of the constructed minimal operator \(L_{\min}\) by a family of operators from the same class, in particular, with smooth coefficients. Under the assumption that the minimal operator is symmetric, the authors describe all its selfadjoint, maximal dissipative, and maximal accumulative extensions in terms of homogeneous boundary conditions of the canonical form. These extensions are parametrized, respectively, by the unitary operators and by the contraction operators in \(\mathbb{C}^m\). The suggested parametrization is bijective and continuous.
Mathematics Subject Classification ID: 47A52
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 6110034
zbMATH Keywords: regularization
zbMATH Keywords: singular Sturm-Liouville problem
zbMATH Keywords: maximal operators
zbMATH Keywords: minimal operators
zbMATH Keywords: selfadjoint extensions
zbMATH Keywords: maximal dissipative extensions
zbMATH Keywords: maximal accumulative extensions
zbMATH Keywords: uniform resolvent approximation
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: s11253-012-0584-6
OpenAlex ID: W2020394432
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DOI: 10.1007/S11253-012-0584-6
description: scientific article; zbMATH DE number 6110034