Results 61 to 70 of about 9,965 (190)
, 2013 We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the spectrum of the ...
Ngoc, San Vũ +2 more
core +3 more sources
Pseudodifferential Operators with Rough Symbols [PDF]
Journal of Fourier Analysis and Applications, 2009 In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale invariant quantities involving the symbols.
openaire +2 more sources
The Metivier inequality and ultradifferentiable hypoellipticity
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
wiley +1 more source
An index formula for perturbed Dirac operators on Lie manifolds
, 2013 International ...
Carvalho, C., Nistor, V.
core +3 more sources
Invariant distributions and the transport twistor space of closed surfaces
Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.Abstract We study transport equations on the unit tangent bundle of a closed oriented Riemannian surface and their links to the transport twistor space of the surface (a complex surface naturally tailored to the geodesic vector field). We show that fibrewise holomorphic distributions invariant under the geodesic flow — which play an important role in ...
Jan Bohr +2 more
wiley +1 more source
Spectral Riesz-Cesaro means: How the square root function helps us to see around the world
Electronic Journal of Differential Equations, 2000 The heat-kernel expansion for a nonanalytic function of a differential operator, and the integrated (Cesà ro-smoothed) spectral densities associated with the corresponding nonanalytic function of the spectral parameter, exhibit a certain nonlocal ...
S. A. Fulling +2 more
doaj
MathematicsWe describe the Friedrichs extension of elliptic symmetric pseudodifferential operators on a closed smooth manifold with the domain consisting of functions vanishing on a given submanifold.
Anton Savin
doaj +1 more source
Korteweg–de Vries waves in peridynamical media
Studies in Applied Mathematics, Volume 152, Issue 1, Page 376-403, January 2024.Abstract We consider a one‐dimensional peridynamical medium and show the existence of solitary waves with small amplitudes and long wavelength. Our proof uses nonlinear Bochner integral operators and characterizes their asymptotic properties in a singular scaling limit.
Michael Herrmann, Katia Kleine
wiley +1 more source
Prediction Method of Maximum Propagation Angle in Parabolic Equation Model over Irregular Terrain
International Journal of Antennas and Propagation, Volume 2024, Issue 1, 2024.The parabolic equation (PE) model is effective for predicting signal propagation over irregular terrains. The shift map method of the PE model is highly accurate and widely used for terrain propagation predictions. The maximum propagation angle is a crucial parameter of the shift map model.
Rui Zhang +5 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, 2007 The regularity of solutions to variational inequalities involving local operators has been studied extensively. Less attention has been paid to those involving nonlocal pseudodifferential operators. We present two regularity results for such problems.
Randolph G. Cooper
doaj +1 more source