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Johannes Sjoestrand

Publications and source records attributed to Johannes Sjoestrand.

60 records · Page 4Linked to original sources
arXiv2003

Perturbations of selfadjoint operators with periodic classical flow

We consider non-selfadjoint perturbations of a self-adjoint $h$-pseudodifferential operator in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength $ε$ of the perturbation satisfies $h^{δ_0} <ε\le ε_0$ for some $δ_0\in ]0,1/2[$ and a sufficiently small $ε_0>0$. We get a complete asymptotic description of all eigenvalues in certain rectangles $[-1/C,1/C]+iε[F_0-1/C,F_0+1/C]$. In particular we are able to treat the case when $ε>0$ is small but independent of $h$.

math.SP↗
arXiv2003

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.

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arXiv2003

Non-selfadjoint perturbations of selfadjoint operators in 2 dimensions I

This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength $ε$ of the perturbation is $\gg h$ (or sometimes only $\gg h^2$) and bounded from above by $h^δ$ for some $δ>0$. We get a complete asymptotic description of all eigenvalues in certain rectangles $[-1/C, 1/C]+ iε[F_0-1/C,F_0+1/C]$.

math.SP↗
arXiv2002

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.

math.SP↗
arXiv2001

Quantum monodromy and semi-classical trace formulae

Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is described in terms of closed orbits of the corresponding classical Hamiltonian. In algebraic situations, such as the original Selberg trace formula, the identities are exact, while in general they hold only in semi-classical or high-energy limits. We refer to a recent survey \cite{Ur} for an introduction and references. In this paper we present an intermediate trace formula in which the original trace is expressed in terms of traces of quantum monodromy operators directly related to the classical dynamics. The usual trace formulae follow and in addition this approach allows handling effective Hamiltonians.

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