What question did this study set out to answer?

To establish that the eigenfunctions derived from selfadjoint Dirac operators form a Riesz basis in a specific Hilbert space.

March 10, 2026

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Riesz Bases Generated by the Spectra of Dirac Operators

THT. N. HarutyunyanYerevan State University

Key Points

To establish that the eigenfunctions derived from selfadjoint Dirac operators form a Riesz basis in a specific Hilbert space.
Analyzed eigenvalues from selfadjoint Dirac operators on the interval (0, π)
Constructed a system of functions based on these eigenvalues
Employed properties of Hilbert spaces to show conditions for Riesz bases.
The functions formed a Riesz basis in the Hilbert space L²([0, π])
Confirmed the completeness and linear independence of the generated functions.

Abstract

We prove, that if \₍\₍ ₙ is the set of eigenvalues of selfadjoint Dirac operator on (0, ), then the system \ (matrix₍x\\ -₍xmatrix) \₍ ₙ is a Riesz bases in Hilbert space L^2 (0, ), C^2).

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اسأل الذكاء الاصطناعي

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View Full Paper

Riesz Bases Generated by the Spectra of Dirac Operators

Key Points

Abstract

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