Similar transformation of one class of correct restrictions
B.N. Biyarov
TL;DR
This paper investigates correct restrictions of the maximal operator in a Hilbert space, introduces a class with similar transformations, and applies the results to n-order differentiation operators with singular coefficients.
Contribution
It identifies a class of correct restrictions with similar transformations and applies this to study differentiation operators with singular coefficients.
Findings
Established a class of correct restrictions with similar transformations.
Applied the theorem to n-order differentiation operators with singular coefficients.
Provided a framework for analyzing restrictions of maximal operators in Hilbert spaces.
Abstract
The description of all correct restrictions of the maximal operator are considered in a Hilbert space. A class of correct restrictions are obtained for which a similar transformation has the domain of the fixed correct restriction. The resulting theorem is applied to the study of n-order differentiation operator with singular coefficients.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Matrix Theory and Algorithms