Estimates of Riesz Constants for the Dirac System with an Integrable Potential

Abstract

We consider the Dirac operator on the interval [0, π] with an integrable potential P = (p_ij (x))_i,j=1² and strongly regular boundary conditions U. It is well known that for any integrable potential P the system {y_n}_n∈Z of root functions of the strongly regular operator L_P,U is a Riesz basis in the space H = L₂[0, π] × L₂[0, π]. We obtain estimates, uniform on every compact set of potentials, of the Riesz constants ||T||||T⁻¹||, where T is the operator of transition to an orthonormal basis.