The Asymptotic Distribution of Eigenvalues of Partial Differential Operators

Lower bounds for the spectral function and for the remainder in local Weyl’s law on manifolds

“…The upper bounds for R(λ) and R x (λ) are attained for round spheres and hence are sharp. Both local and integrated remainder estimates for the Weyl's law on manifolds under various geometric conditions have been actively studied in the last forty years (see [2], [8], [10], [14], [21], [24], [26], [29], [31], etc).…”

The Berezin and Garding Inequalities

“…for every B ∈ Ψ m provided that n+m−1 0, where σ A and σ B are principal symbols of the operators A and B (see, for example, [7] or [11]). …”

Preface to the Special Issue in Memory of Yuri Safarov

“…Furthermore, under the nonperiodicity condition (not too many periodic billiard trajectories, see [16] for details) Safarov proved the stronger result…”

“…We finished writing our book [16] in 1996. The book deals with an elliptic self-adjoint scalar differential operator of even order 2m acting on half-densities over a compact n-dimensional manifold M with smooth boundary ∂M , subject to m boundary conditions on ∂M .…”

“…In the latter part of his career, after finishing the book [16], Yuri studied a variety of different questions in the spectral theory of differential operators. Some of these publications are mentioned below.…”