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Differential Equations

, Volume 55, Issue 5, pp 631–643 | Cite as

Basis Properties of Root Functions of Differential Operators with Spectral Parameter in the Boundary Conditions

  • A. A. ShkalikovEmail author
Ordinary Differential Equations

Abstract

Let B = BCN be a finite-dimensional extension of a Banach space B, and let B be equipped with the norm ||u|| = (||u||2 + ||a||2)1/2, where u = {u, a}, uB, aCN. The element u is called the projection of u onto B. We find a criterion for the simultaneous completeness and minimality (respectively, for the basis property) of the system {uk}k=N+18 of projections under the condition that the system {uk}k=18 is complete and minimal (respectively, is a basis) in the space B. This criterion is used to study the basis property of root functions of second- and fourth-order ordinary differential operators in the space L2.

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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