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Plancherel Type Estimates and Sharp Spectral Multipliers
Abstract We study general spectral multiplier theorems for self-adjoint positive definite operators on L2(X,μ), where X is any open subset of a space of homogeneous type. We show that the sharpExpand
Categorification of the Kauffman bracket skein module of I-bundles over surfaces
Khovanov defined graded homology groups for links LR 3 and showed that their polynomial Euler characteristic is the Jones polyno- mial of L. Khovanov's construction does not extend in aExpand
On skein algebras and Sl2(C)-character varieties
Let M be an oriented 3-manifold. For any commutative ring R with a speci"ed invertible element A one can assign an R-moduleS 2,= (M; R, A) called the Kau!man bracket skein module of M. This invariantExpand
Topology on the Spaces Of Orderings of Groups
A natural topology on the space of left orderings of an arbitrary semi-group is introduced here. This space is proved to be compact, and for free abelian groups it is shown to be homeomorphic to theExpand
Riesz transform, Gaussian bounds and the method of wave equation
Abstract.For an abstract self-adjoint operator L and a local operator A we study the boundedness of the Riesz transform AL−α on Lp for some α > 0. A very simple proof of the obtained result is basedExpand
Character Varieties
Let G be a complex reductive algebraic group and let Γ be a finitely generated group. We study properties of irreducible and completely reducible representations ρ : Γ → G in the context of theExpand
Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analyticExpand
Multivariable Spectral Multipliers and Analysis of Quasielliptic Operators on Fractals
We study multivariable spectral multipliers F(L 1 , L 2 ) acting on the Cartesian product of ambient spaces of two self-adjoint operators L 1 and L 2 . We prove that ifF satisfies Hormander typeExpand
Imaginary powers of Laplace operators
We show that if L is a second-order uniformly elliptic operator in divergenceformonRd, then Ci(1+lol)d/2 < |ILi'I|,1-L,,. <? C2(1+1kaI)d/2. We also prove that the upper bounds remain true for anyExpand
Restriction and spectral multiplier theorems on asymptotically conic manifolds
The classical Stein-Tomas restriction theorem is equivalent to the statement that the spectral measure $dE(\lambda)$ of the square root of the Laplacian on $\RR^n$ is bounded from $L^p(\RR^n)$ toExpand