Spectral Properties of the Schrödinger Operator with $\delta$-Distribution

For the one-dimensional Schrödinger operator with $\delta$-interactions, two-sided estimates of the distribution function of the eigenvalues and a criterion for the discreteness of the spectrum in terms of the Otelbaev function are obtained. A criterion for the resolvent of the Schrödinger operator to belong to the class $\mathfrak S_p$ is established.