On the Equiconvergence Rate with the Fourier Integral of the Spectral Expansion Associated with the Self-Adjoint Extension of the Sturm_Liouville Operator with Uniformly Locally Integrable Potential

摘要

In the space L2(R), we consider the self-adjoint extension L of the Sturm_Liouville operator ly = _y + q(x)y whose potential q is uniformly locally integrable on R, i.e., satisfies the condition ωq(h) = sup x∈R x+h x |q(t)| dt < +∞, h>0. oWf easftuundcytitohne fpr∈obLle1m(Ro)nwthitehetqhueicFoonuvreiregrenincteegraratel oonf tthheesepnetcitrrealreeaxlplainnsei.onWaessoobctiaatineduwniiftohrmL estimates of the equiconvergence rate under some additional conditions on f or q.