Search results for " Operator"
showing 10 items of 931 documents
Pseudodifferential operators on manifolds with a Lie structure at infinity
2003
to appear in Anal. Math.; Several examples of non-compact manifolds $M_0$ whose geometry at infinity is described by Lie algebras of vector fields $V \subset \Gamma(TM)$ (on a compactification of $M_0$ to a manifold with corners $M$) were studied by Melrose and his collaborators. In math.DG/0201202 and math.OA/0211305, the geometry of manifolds described by Lie algebras of vector fields -- baptised "manifolds with a Lie structure at infinity" there -- was studied from an axiomatic point of view. In this paper, we define and study the algebra $\Psi_{1,0,\VV}^\infty(M_0)$, which is an algebra of pseudodifferential operators canonically associated to a manifold $M_0$ with the Lie structure at …
Partial data inverse problems for the Hodge Laplacian
2017
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…
Manifolds with vectorial torsion
2015
Abstract The present note deals with the properties of metric connections ∇ with vectorial torsion V on semi-Riemannian manifolds ( M n , g ) . We show that the ∇-curvature is symmetric if and only if V ♭ is closed, and that V ⊥ then defines an ( n − 1 ) -dimensional integrable distribution on M n . If the vector field V is exact, we show that the V-curvature coincides up to global rescaling with the Riemannian curvature of a conformally equivalent metric. We prove that it is possible to construct connections with vectorial torsion on warped products of arbitrary dimension matching a given Riemannian or Lorentzian curvature—for example, a V-Ricci-flat connection with vectorial torsion in di…
Notes on bilinear multipliers on Orlicz spaces
2019
Let $\Phi_1 , \Phi_2 $ and $ \Phi_3$ be Young functions and let $L^{\Phi_1}(\mathbb{R})$, $L^{\Phi_2}(\mathbb{R})$ and $L^{\Phi_3}(\mathbb{R})$ be the corresponding Orlicz spaces. We say that a function $m(\xi,\eta)$ defined on $\mathbb{R}\times \mathbb{R}$ is a bilinear multiplier of type $(\Phi_1,\Phi_2,\Phi_3)$ if \[ B_m(f,g)(x)=\int_\mathbb{R} \int_\mathbb{R} \hat{f}(\xi) \hat{g}(\eta)m(\xi,\eta)e^{2\pi i (\xi+\eta) x}d\xi d\eta \] defines a bounded bilinear operator from $L^{\Phi_1}(\mathbb{R}) \times L^{\Phi_2}(\mathbb{R})$ to $L^{\Phi_3}(\mathbb{R})$. We denote by $BM_{(\Phi_1,\Phi_2,\Phi_3)}(\mathbb{R})$ the space of all bilinear multipliers of type $(\Phi_1,\Phi_2,\Phi_3)$ and inve…
Fokker–Planck equation with respect to heat measures on loop groups
2011
Abstract The Dirichlet form on the loop group L e ( G ) with respect to the heat measure defines a Laplacian Δ DM on L e ( G ) . In this note, we will use Wasserstein distance variational method to solve the associated heat equation for a given data of finite entropy.
Heat semi-group and generalized flows on complete Riemannian manifolds
2011
Abstract We will use the heat semi-group to regularize functions and vector fields on Riemannian manifolds in order to develop Di Perna–Lions theory in this setting. Malliavinʼs point of view of the bundle of orthonormal frames on Brownian motions will play a fundamental role. As a byproduct we will construct diffusion processes associated to an elliptic operator with singular drift.
Annihilating sets for the short time Fourier transform
2010
Abstract We obtain a class of subsets of R 2 d such that the support of the short time Fourier transform (STFT) of a signal f ∈ L 2 ( R d ) with respect to a window g ∈ L 2 ( R d ) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L 2 -norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces.
Superlinear (p(z), q(z))-equations
2017
AbstractWe consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does not satisfy the Ambrosetti–Rabinowitz condition. The hypotheses on the reaction term ensure that the Euler–Lagrange functional, associated to the problem, satisfies both the -condition and a mountain pass geometry.
The variation of the maximal function of a radial function
2017
We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.
Geometry of spaces of compact operators
2008
We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if $\mathcal{K}(Y,X^{**})\subseteq\mathcal{K}(Y,X)^{**}$ for all reflexive Banach spaces Y. We show that X * has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation prope…