Bessel Property of Nonorthogonal Systems of Cylinder Functions
Д. Ю. Бородинова · Differential Equations · 2020
Abstract For the operator defined by the differential operation $$ Lu=-y^{\prime \prime }+x^{-2}( u ^2-{1}/{4})y,$$$$0< u <1 $$, on the interval $$(0,1) $$, we study the statements of spectral boundary value problems with general boundary conditions at the singular point $$x=0 $$ as well as the basis properties of the systems of cylinder functions arising in these problems. We find sufficient conditions on the spectral parameter under which these systems have the Bessel property in $$L_2(0,1) $$.