On the limiting behaviour of the spectrum of a sequence of operators defined on different Hilbert spaces

Abstract

Abstnft. The theory of the 3-mixing process for thermal collisions between Rydberg atoms and neutral particles has been developed in the impulse approximation using the formalism of spherical tensor operators and the WKB approximation. We have derived a simple formula far the cross section of inelastic nU -"U' transitions, which provides the dependence on the principal n and orbital I quantum numbers, relative velocity V and the energy defect A%,,. of the fine-structure splitting. The analytical results obtained are in good agreement with the available experimental data and numerical calculations.

Periodic elliptic operators with asymptotically preassigned spectrum

“…It is clear that λ 1 = 0 (λ 1 coincides with the first eigenvalue of −b −1 j ∆ N B ) while To complete the proof of lemma we have to prove (3.23). For that we use the following Theorem (see [13]). Let H ε , H 0 be separable Hilbert spaces, let L ε :…”

Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace–Beltrami operator

“…Thus, to complete the proof of the lemma we have to prove (3.29). For that we use the abstract scheme proposed in the work [16].…”

Homogenization of free boundary oscillations of an inviscid fluid in a porous reservoir

“…The conclusions of Theorem 2.1 follow immediately from Lemmas 3.1, 3.3, 3.8 and 3.9, which appear to be the vérifications of assumptions of the mentioned abstract result [4].…”