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Functional calculus for Safarov pseudo-differential operators

Year: 2026

Type: article

Abstract: Given a smooth, closed Riemannian manifold ( M , g ) (M,g) equipped with a linear connection ∇ \nabla (not necessarily metric), we develop the holomorphic functional calculus for operators belonging to the global pseudo-differential classes Ψ ρ , δ m ( Ω κ , ∇ , τ ) \Psi _{\rho , \delta }^m\left (\Omega ^\kappa , \nabla , \tau \right ) introduced by Safarov. As a consequence of our main result, we establish a Szegö type-theorem, derive asymptotic expansion of the heat kernel trace, and calculate some associated spectral ζ \zeta -functions

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9806

Authors: Santiago Gómez Cobos, Michael Ruzhansky

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, Engineering and Physical Sciences Research Council, Bijzonder Onderzoeksfonds UGent

Awards: G1083792743, G2080133828, G2223683291, G2550275140, G256415834, G2745040304, G403754905, G4284836421, G6715076113, G7653587095, Pseudo-differential operators on homogeneous manifolds, Hyperbolic problems with discontinuous coefficients

OpenAlex ID: W4415317468

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