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154
L p spectral theory of higherorder elliptic differential operators
 Bull. London Math. Soc
, 1997
"... 2. Eigenvalues and eigenfunctions 516 2.1 Spectral asymptotics 516 2.2 The isoperimetric problem 518 ..."
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Cited by 17 (1 self)
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2. Eigenvalues and eigenfunctions 516 2.1 Spectral asymptotics 516 2.2 The isoperimetric problem 518
WEYLTITCHMARSH THEORY FOR STURMLIOUVILLE OPERATORS WITH DISTRIBUTIONAL COEFFICIENTS
, 2012
"... We systematically develop Weyl–Titchmarsh theory for singular differential operators on arbitrary intervals (a,b) ⊆ R associated with rather general differential expressions of the type τf = 1 ..."
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Cited by 16 (12 self)
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We systematically develop Weyl–Titchmarsh theory for singular differential operators on arbitrary intervals (a,b) ⊆ R associated with rather general differential expressions of the type τf = 1
Almost periodic solutions of first and secondorder Cauchy problems
 J. Differential Equations
, 1997
"... ..."
A.: Weak Coupling and Continuous Limits for Repeated Quantum Interactions preprint mparc
"... We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical subsystems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the ..."
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We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical subsystems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ 2 τ → 0 and the critical case λ 2 τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a nontrivial invariant subalgebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model whose asymptotic effective evolution is generated by this Lindblad operator. AMS classification numbers: 81Q99
Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections
, 2004
"... ..."
H∞ FUNCTIONAL CALCULUS AND SQUARE FUNCTIONS ON Noncommutative L^Pspaces
, 2006
"... In this work we investigate semigroups of operators acting on noncommutative L pspaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H ∞ functional calculus. We discuss several examples of noncommutative diffusion semig ..."
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Cited by 12 (5 self)
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In this work we investigate semigroups of operators acting on noncommutative L pspaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H ∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, qOrnsteinUhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups.
Nonselfadjoint harmonic oscillator, compact semigroups and pseudospectra
 J. Operator Theory
"... We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. ..."
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We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. The second relies on the fact that the bounded holomorphic semigroup generated by the complex harmonic oscillator is of HilbertSchmidt type in a maximal angular region. In order to show this last property, we deduce a nonselfadjoint version of the classical Mehler’s formula.
New Spectral Criteria for Almost Periodic Solutions of Evolution Equations
"... We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form x = A(t)x+f(t) (), with f having precompact range, which will be then applied to find new spectral criteria for the existence of almost periodic solutions ..."
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Cited by 11 (4 self)
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We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form x = A(t)x+f(t) (), with f having precompact range, which will be then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonnant case where e isp(f) may intersect the spectrum of the monodromy operator P of () (here sp(f) denotes the Carleman spectrum of f ). We show that if () has a bounded uniformly continuous mild solution u and oe \Gamma (P )ne isp(f) is closed, where oe \Gamma (P ) denotes the part of oe(P ) on the unit circle, then () has a bounded uniformly continuous mild solution w such that e isp(w) = e isp(f) . Moreover, w is a "spectral component" of u. This allows to solve the general Masseratyped problem for almost periodic solutions. Various spectral criteria for the existence of almost periodic, quasiperiodic mild solutions to () are ...
Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics. Random Oper. Stochastic Equations
"... A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in Rd which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure µ as invariant measure. We study a scaling limit of such a dynamics, where the ..."
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Cited by 10 (5 self)
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A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in Rd which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure µ as invariant measure. We study a scaling limit of such a dynamics, where the scaling is of Kac type. Informally, we expect that, in the limit, only jumps of “infinite length ” will survive, i.e., we expect to arrive at a Glauber dynamics in continuum (a birthanddeath process in Rd). We prove that, in the low activityhigh temperature regime, the generators of the Kawasaki dynamics converge to the generator of a Glauber dynamics. The convergence is on the set of exponential functions, in the L2(µ)norm. Furthermore, additionally assuming that the potential of pair interaction is positive, we prove the weak convergence of the finitedimensional distributions of the processes.