2015/07/22 by Benjamin Küster, Küster, Benjamin · 1 citation
Mathematics · #47G30 #58J40 #81Q20 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:47G30 #msc:58J40 #msc:81Q20
paper · pdf · doi:10.48550/arxiv.1507.06214
v2: minor corrections, 33 pages
arxiv created 2016/02/12 · arxiv updated 2016/02/15
We study the functional calculus for operators of the form fh(P(h)) within the theory of semiclassical pseudodifferential operators, where \fh\h∈ (0,1]⊂ C^∞c(ℝ) denotes a family of h-dependent functions satisfying some regularity conditions, and P(h) is either an appropriate self-adjoint semiclassical pseudodifferential operator in L2(ℝn) or a Schrödinger operator in L2(M), M being a closed Riemannian manifold of dimension n. The main result is an explicit semiclassical trace formula with remainder estimate that is well-suited for studying the spectrum of P(h) in spectral windows of width of order hδ, where 0≤ δ<(1)/(2).