Riesz basis of root vectors of a non-symmetric system of first-order ordinary differential operators and application to inverse eigenvalue problems

Abstract

We consider a nonsymmetric first order differential operator

where P is a 2 × 2 matrix whose compnents are of C¹ class on [0,1]. We study an eigenvalue problem for A with boundary conditions at x=0,1. We establish an asympotic form of the eigenvalues and prove that the set of the root vectors forms a Riesz basis in {l²(0,1)}². Next we apply the Riesz basis for showing the uniqueness in inverse eigenvalue problems for nonsymmetric systems. The key is the transformation formula.

Keywords:

• Riesz basis
• Generalized eigenfunction
• Nonsymmetric system
• Inverse eigenvalue problem

AMS:

• 34A55
• 34L10
• 34L20

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Notes

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^† [email protected]