Separability and Estimates for Eigenvalues and Singular Numbers of a Class of Hyperbolic‐Type Differential Operators

ABSTRACT In this paper, we study the spectral properties of a class of differential operators of hyperbolic type with variable unbounded coefficients. We find conditions for the existence of a resolvent and maximum regularity of solutions. We also find conditions that ensure the compactness of the resolvent. We obtain two‐sided estimates of approximation numbers (c‐numbers). In addition, we give an example showing how to find estimates of eigenvalues using estimates of approximation numbers.