Abstract
Let B = B ⊕ CN 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}, u ∈ B, a ∈ CN. 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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