Expand all Collapse all | Results 1 - 4 of 4 |
1. CJM 2011 (vol 63 pp. 961)
Low Frequency Estimates for Long Range Perturbations in Divergence Form We prove a uniform control as $ z \rightarrow 0 $ for the resolvent $
(P-z)^{-1} $ of long range perturbations $ P $ of the Euclidean
Laplacian in divergence form by combining positive commutator
estimates and properties of Riesz transforms. These estimates hold in
dimension $d \geq 3 $ when $ P $ is defined on $ \mathbb{R}^d $ and in dimension $ d \geq 2 $ when $ P $ is defined outside a compact obstacle with Dirichlet boundary conditions.
Keywords:resolvent estimates, thresholds, scattering theory, Riesz transform Category:35P25 |
2. CJM 2007 (vol 59 pp. 742)
Geometry and Spectra of Closed Extensions of Elliptic Cone Operators We study the geometry of the set of closed extensions of index $0$ of
an elliptic differential cone operator and its model operator in
connection with the spectra of the extensions, and we give a necessary
and sufficient condition for the existence of rays of minimal growth
for such operators.
Keywords:resolvents, manifolds with conical singularities, spectral theor, boundary value problems, Grassmannians Categories:58J50, 35J70, 14M15 |
3. CJM 2005 (vol 57 pp. 771)
The Resolvent of Closed Extensions of Cone Differential Operators We study closed extensions $\underline A$ of
an elliptic differential operator $A$ on a manifold with conical
singularities, acting as an unbounded operator on a weighted $L_p$-space.
Under suitable conditions we show that the resolvent
$(\lambda-\underline A)^{-1}$ exists
in a sector of the complex plane and decays like $1/|\lambda|$ as
$|\lambda|\to\infty$. Moreover, we determine the structure of the resolvent
with enough precision to guarantee existence and boundedness of imaginary
powers of $\underline A$.
As an application we treat the Laplace--Beltrami operator for a metric with
straight conical degeneracy and describe domains yielding
maximal regularity for the Cauchy problem $\dot{u}-\Delta u=f$, $u(0)=0$.
Keywords:Manifolds with conical singularities, resolvent, maximal regularity Categories:35J70, 47A10, 58J40 |
4. CJM 2001 (vol 53 pp. 310)
On a Product Related to the Cubic Gauss Sum, III We have seen, in the previous works [5], [6], that the argument of a
certain product is closely connected to that of the cubic Gauss sum.
Here the absolute value of the product will be investigated.
Keywords:Gauss sum, Lagrange resolvent Categories:11L05, 11R33 |