An estimate, in the metric of \(L_2(R)\), of the equiconvergence rate with the Fourier integral for the spectral expansion corresponding to the Schrödinger operator with a potential of a class \(L_1(R)\) (Q5926552)

In the previous paper [Equiconvergence of the Fourier integral with the spectral expansion corresponding to a Schrödinger operator with integral potential. (Russian, English) Differ. Equations 34, No. 8, 1046-1051 (1998); translation from Differ. Uravn. 34, No. 8, 1043-1048 (1998; Zbl 1122.34346)], the author established a series representation of the spectral projection for the positive Schrödinger operator \(l(u)= -u''+ qu\) on the real line with potential \(q\in L_1(\mathbb{R})\), and investigated the convergence of the series in \(L_\infty(\mathbb{R})\). Here, an estimate on the norm of the general term of the series in \(L_2(\mathbb{R})\) is given.