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The present article is concerned with global subelliptic estimates for Kramers–Fokker–Planck operators with polynomials of degree less than or equal to two. The constants appearing in those estimates are accurately formulated in terms of the coefficients, especially when those are large. [ABSTRACT FROM AUTHOR]

Artificial interface conditions parametrized by a complex number θ0 are introduced for 1D-Schrödinger operators. When this complex parameter equals the parameter θ ∈ iℝ of the complex deformation which unveils the shape resonances, the Hamiltonian becomes dissipative. This makes possible an adiabatic theory for the time evolution of resonant states for arbitrarily large time scales. The effect of the artificial interface conditions on the important stationary quantities involved in quantum transport models is also checked to be as small as wanted, in the polynomial scale (hN)N∈ℕ as h → 0, according to θ0. [ABSTRACT FROM AUTHOR]

Initially motivated by a problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator on , where f is a real-valued function and is a small parameter. We define as the infimum of the real part of the spectrum of , and as the supremum of the norm of the resolvent of along the imaginary axis. Under appropriate conditions on f, we show that both quantities and go to infinity as , and we give precise estimates of the growth rate of . We also provide an example where if is small. Our main results are established using variational “hypocoercive” methods, localization techniques, and semiclassical subelliptic estimates. [ABSTRACT FROM PUBLISHER]

We study the compactness of the resolvent of Witten Laplacians on 0-forms and more generally the validity of the Poincaré inequality for Dirichlet forms in finite dimension. We are interested in the case where some known sufficient condition becomes degenerate. For some classes of polyhomogeneous functions, we get simple conditions which are necessary and sufficient for the Poincaré inequality. [ABSTRACT FROM AUTHOR]