A criterion for the resolvent of a Sturm-Liouville operator to be kernel

Spaces admissible for the Sturm-Liouville equation

“…Otelbaev (see [14]), respectively. Analysing our assertions and requirements (see §4 below), it is useful to take into account that the function q * (x)…”

“…Two-sided, sharp by order estimates of the function ρ were first obtained by M. Otelbaev (see [14]), and therefore all such inequalities are referred to by his name. Note that the inequalities given in [14] are expressed in terms of another auxiliary function, more complicated than d(x), x ∈ R, and are proven under auxiliary requirements to the function q.…”

A criterion for compactness in Lp(ℝ) of the resolvent of the maximal general form Sturm–Liouville operator

“…Remark 2.7 (Chernyavskaya and Shuster [2]). Two-sided sharp-by-order a priori estimates of the function ρ first appeared in Otelbaev's paper, [16] (under some additional requirements for r and q). Therefore, we call inequalities of such a form Otelbaev inequalities.…”

Spectral properties of a class of singular differential operators

“…From (6), (12), and (15) it easily follows In each of the representations (6), (12), and (15) there are n constants: in the…”

“…[2], [3], and the references given their. A special method to study spectral properties presented in this paper can be found, for example, in [1], [11], and [12]. In the monographs [8], [13] a complete presentation of this method is given and applied.…”