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We study a geometric generalization of the time-dependent Schrödinger equation for the harmonic oscillator $(D_{t} + \frac{1}{2} Δ + V) ψ = 0 (0.1)$ where $Δ$ is the Laplace-Beltrami operator with respect to a “scattering metric” on a compact manifold $M$ with boundary (the class of scattering metrics is a generalization of asymptotically Euclidean metrics on $ℝ^{n}$ , radially compactified to the ball) and $V$ is a perturbation of $\frac{1}{2} ω^{2} x^{- 2}$ , with $x$ a boundary defining function for $M$ (e.g. $x = 1 / r$ in the compactified Euclidean case). Using the quadratic-scattering...

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The index of transversally elliptic complexes

The Kashiwara cojugation and wave-front sets of regular holonomic distributions on a complex manifold.

The Kashiwara conjugation and wave-front sets of regular holonomic distributions on a complex manifold (Erratum).

The propagation of polarization in double refraction

The reconstruction theorem ℳ ∞ = ℰ ∞ ⊗ ℰ ℳ r e g

The regularity of convolution and restriction of distributions

The trace of the generalized harmonic oscillator

Currently displaying 1 – 7 of 7

The reconstruction theorem $ℳ^{\infty} = ℰ^{\infty} \otimes_{ℰ} ℳ_{r e g}$