L _μ → L _ν equiconvergence of spectral decompositions for a Dirac system with L _κ potential

Abstract

It is proved that if P ∈ L _κ[0, π], κ ∈ (1, ∞], then the expansions of any function f ∈ L _μ[0, π], μ ∈ [1, ∞], in the generalized eigenfunctions of the perturbed and unperturbed operators are equiconvergent in the norm of the space L _ν[0, π], provided that ν ∈ [1, ∞] satisfies the inequality $\frac{1}{\kappa } + \frac{1}{\mu } - \frac{1}{\nu } \leqslant 1$, except in the case where κ = ν = ∞ and μ = 1.