Results 41 to 50 of about 460 (55)

Birkhoff normal forms for Fourier integral operators II [PDF]

arXiv, 2001
In this work we construct logarithms and Birkhoff normal forms for elliptic Fourier integral operators in the semi-classical limit under more general assumptions than in aprevious work by the first author. The methods are similar but slightly different.
arxiv  

$L^p - L^{p'}$ estimates for overdetermined Radon transforms [PDF]

arXiv, 2003
We prove several variations on the results of Ricci and Travaglini concerning bounds for convolution with all rotations of a measure supported by a fixed convex curve in the plane. Estimates are obtained for averages over higher-dimensional convex hypersurfaces, smooth k-dimensional surfaces and non-translation invariant families of surfaces.
arxiv  

Survey of the inverse spectral problem [PDF]

Surveys in differential geometry. Vol. IX, 401--467 (2004), 2004
This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete inverse spectral problems.
arxiv  

Bohr-Sommerfeld conditions for several commuting Hamiltonians

, 2002
The goal of this paper is to find the quantization conditions of Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of dimension n, depending on a small parameter h, and which commute to each other.
Anne, C., Charbonnel, A-M.
core   +1 more source

Structure of the Short Range Amplitude for General Scattering Relations [PDF]

arXiv, 2004
We consider scattering by short range perturbations of the semi-classical Laplacian. We prove that when a polynomial bound on the resolvent holds, the scattering amplitude is a semi-classical Fourier integral operator associated to the scattering relation. Compared to previous work, we allow the scattering relation to have more general structure.
arxiv  

Logarithmic Trace of Toeplitz Projectors [PDF]

arXiv, 2004
We prove that the trace of the logarithmic term of the Toeplitz kernel on a contact manifold is a contact invariant, generalizing K. Hirachi's invariant for the Szego kernel on a CR manifold. When the base manifold is the three-sphere, this vanishes identically.
arxiv  

Multidimensional decay in van der Corput lemma [PDF]

Studia Math., 208 (2012), 1-10, 2007
In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard one-dimensional van der Corput lemma with the stationary phase method.
arxiv  

On local and global regularity of Fourier integral operators [PDF]

New developments in pseudo-differential operators, 185-200, Oper. Theory Adv. Appl., 189, Birkhauser, Basel, 2009., 2008
The aim of this paper is to give a review of local and global properties of Fourier integral operators with real and complex phases, in local $L^p$, global $L^2$, and in Colombeau's spaces.
arxiv  

Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators [PDF]

arXiv, 2008
Following the work of Duistermaat-Singer \cite{DS} on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we show that any such isomorphism is given by conjugation by $A = BF$, where $B$ is a microlocally elliptic ...
arxiv  

The truncated Fourier operator. VI [PDF]

arXiv, 2009
The spectral analysis of the Fourier operator truncated on the positive half-axis is ...
arxiv