A New Estimate for the Spectral Function of the Self-Adjoint Extension in L2(R) of the Sturm-Liouville Operator with a Uniformly Locally Integrable Potential

摘要

In the space L_2(R), we consider the self-adjoint extension L of the Sl.urni Lkmvillc operator ly = -y" + q(x)y whose potential q is uniformly locally integral >le on lit, i.e., wilisfius the eundition ω(h)=sup_(x∈R) ∫_x~(x+h) |q(t)|dt<+∞, h>0. (1)The uniqueness of a self-adjoint extension under condition (1) and I.lie lower seitiibniintlcdtKWH of the operator Sf were proved in [1, Chap. 1].