Pseudodifferential operators and weighted normed symbol spaces

In this work we study some general classes of pseudodifferential operators whose symbols are defined in terms of phase space estimates

Elementary linear algebra for advanced spectral problems

We discuss the general method of Grushin problems, closely related to Shur complements, Feshbach projections and effective Hamiltonians, and describe various appearances in spectral theory, pdes, mathematical physics and numerical problems.Comment: 2 figure

Resonances associated to a closed hyperbolic trajectory in dimension 2

We consider resonances in the semi-classical limit, generated by a single closed hyperbolic orbit, for an operator on ${\bf R}^2$. We determine all such resonancess in a domain independent of the semi-classical parameter As an application we determine all resonances generated by a saddle point in a fixed disc around the critical energy

Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators