180 research outputs found
The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
For any orientable compact surface with boundary, we compute the regularized
determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values
of dynamical zeta functions by using natural uniformizations, one due to
Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any
dimension the DN map for the Yamabe operator to the scattering operator for a
conformally compact related problem by using uniformization.Comment: 16 page
The Selberg zeta function for convex co-compact Schottky groups
We give a new upper bound on the Selberg zeta function for a convex
co-compact Schottky group acting on : in strips parallel to
the imaginary axis the zeta function is bounded by
where is the dimension of the limit set of the group. This bound is
more precise than the optimal global bound , and it gives
new bounds on the number of resonances (scattering poles) of . The proof of this result is based on the
application of holomorphic -techniques to the study of the determinants
of the Ruelle transfer operators and on the quasi-self-similarity of limit
sets. We also study this problem numerically and provide evidence that the
bound may be optimal. Our motivation comes from molecular dynamics and we
consider as the simplest model of
quantum chaotic scattering. The proof of this result is based on the
application of holomorphic -techniques to the study of the determinants of
the Ruelle transfer operators and on the quasi-self-similarity of limit sets
Analytic Continuation of Resolvent Kernels on noncompact Symmetric Spaces
Let X=G/K be a symmetric space of noncompact type and let L be the Laplacian
associated with a G-invariant metric on X. We show that the resolvent kernel of
L admits a holomorphic extension to a Riemann surface depending on the rank of
the symmetric space. This Riemann surface is a branched cover of the complex
plane with a certain part of the real axis removed. It has a branching point at
the bottom of the spectrum of L. It is further shown that this branching point
is quadratic if the rank of X is odd, and is logarithmic otherwise. In case G
has only one conjugacy class of Cartan subalgebras the resolvent kernel extends
to a holomorphic function on a branched cover of the complex plane with the
only branching point being the bottom of the spectrum.Comment: 16 pages, 3 figures, LaTe
Isoresonant complex-valued potentials and symmetries
Let be a connected Riemannian manifold such that the resolvent of the
free Laplacian (\Delta-z)^{-1}, z\in\C\setminus\R^{+}, has a meromorphic
continuation through . The poles of this continuation are called
resonances. When has some symmetries, we construct complex-valued
potentials, , such that the resolvent of , which has also a
meromorphic continuation, has the same resonances with multiplicities as the
free Laplacian.Comment: 32 page
The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem and its applications
We introduce a class of functions near zero on the logarithmic cover of the
complex plane that have convergent expansions into generalized power series.
The construction covers cases where non-integer powers of and also terms
containing can appear. We show that under natural assumptions some
important theorems from complex analysis carry over to the class of these
functions. In particular it is possible to define a field of functions that
generalize meromorphic functions and one can formulate an analytic Fredholm
theorem in this class. We show that this modified analytic Fredholm theorem can
be applied in spectral theory to prove convergent expansions of the resolvent
for Bessel type operators and Laplace-Beltrami operators for manifolds that are
Euclidean at infinity. These results are important in scattering theory as they
are the key step to establish analyticity of the scattering matrix and the
existence of generalized eigenfunctions at points in the spectrum.Comment: 27 page
Une chaßne de traitement de l'information géographique au service de l'application de la loi Littoral
Lâapplication de la loi Littoral nĂ©cessitait une approche nouvelle de la part de lâĂtat et la mise en Ćuvre dâoutils nouveaux pour une gestion Ă long terme. Lâapport de traitements automatiques de lâinformation gĂ©ographique a Ă©tĂ© ainsi testĂ© au CETE Normandie-Centre sur trois des grands principes posĂ©s par cette loi
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
We establish a limiting absorption principle for Dirichlet Laplacians in
quasi-cylindrical domains. Outside a bounded set these domains can be
transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet
Laplacians model quantum or acoustically-soft waveguides associated with
quasi-cylindrical domains. We construct a uniquely solvable problem with
perfectly matched layers of finite length. We prove that solutions of the
latter problem approximate outgoing or incoming solutions with an error that
exponentially tends to zero as the length of layers tends to infinity. Outgoing
and incoming solutions are characterized by means of the limiting absorption
principle.Comment: to appear in SIAM Journal on Mathematical Analysi
Hugo Vermeren, Les Italiens à BÎne (1865-1940). Migrations méditerranéennes et colonisation de peuplement en Algérie, Rome
Les Italiens Ă BĂŽne (1865-1940) est le fruit dâune thĂšse soutenue en 2015. Lâauteur a portĂ© son attention sur les foisonnants devenirs urbains et français de plusieurs milliers de migrants italiens et de leurs descendants installĂ©s Ă BĂŽne (actuelle Annaba), alors principal port de lâEst algĂ©rien. Le rĂ©cit fait constamment varier les Ă©chelles dâanalyse. Lâarticulation entre histoire de lâimmigration et histoire de la colonisation, trop souvent dĂ©liĂ©es, nâest pas la moindre des rĂ©ussites de ce ..
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