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http://hdl.handle.net/2440/299
Mon, 01 Sep 2014 07:37:01 GMT2014-09-01T07:37:01ZSemiclassical Lᵖ estimates of quasimodes on curved hypersurfaces
http://hdl.handle.net/2440/84772
Title: Semiclassical Lᵖ estimates of quasimodes on curved hypersurfaces
Author: Hassell, A.; Tacy, M.
Abstract: Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L p norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch −δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator. In this article, we assume that H is a hypersurface, and make the additional geometric assumption that H is curved (in the sense of Definition 2.6 below) with respect to the bicharacteristic flow of P. Under this assumption we improve the estimate from δ=1/4 to 1/6, generalizing work of Burq–Gérard–Tzvetkov and Hu for Laplace eigenfunctions. To do this we apply the Melrose–Taylor theorem, as adapted by Pan and Sogge, for Fourier integral operators with folding canonical relations.Sat, 31 Dec 2011 13:30:00 GMThttp://hdl.handle.net/2440/847722011-12-31T13:30:00ZDécalage and Kan's simplicial loop group functor
http://hdl.handle.net/2440/84750
Title: Décalage and Kan's simplicial loop group functor
Author: Stevenson, D.Sat, 31 Dec 2011 13:30:00 GMThttp://hdl.handle.net/2440/847502011-12-31T13:30:00ZCross-separatrix flux in time-aperiodic and time-impulsive flows
http://hdl.handle.net/2440/84746
Title: Cross-separatrix flux in time-aperiodic and time-impulsive flows
Author: Balasuriya, S.
Abstract: A theory for the fluid flux generated across heteroclinic separatrices under the influence of time-aperiodic perturbations is presented. The flux is explicitly defined as the amount of fluid transferred per unit time, and its detailed time-dependence monitored. The perturbations are allowed to be significantly discontinuous in time, including for example impulsive (Dirac delta type) discontinuities. The flux is characterized in terms of time-varying separatrices, with easily computable formulae (directly related to Melnikov functions) provided.Sat, 31 Dec 2005 13:30:00 GMThttp://hdl.handle.net/2440/847462005-12-31T13:30:00ZAnalytic torsion for twisted de Rham complexes
http://hdl.handle.net/2440/84726
Title: Analytic torsion for twisted de Rham complexes
Author: Varghese, M.; Wu, S.Fri, 31 Dec 2010 13:30:00 GMThttp://hdl.handle.net/2440/847262010-12-31T13:30:00Z