Related papers: On $L^p$ resolvent estimates for Laplace-Beltrami …

We prove uniform $L^p$ estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul of [3] in the case of Laplace-- Beltrami operators on…

We prove $L^p\to L^{p'}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has the same behavior with respect to the spectral parameter $z$…

We address an interesting question raised by Dos Santos Ferreira, Kenig and Salo about regions ${\mathcal R}_g\subset {\mathbb C}$ for which there can be uniform $L^{\frac{2n}{n+2}}\to L^{\frac{2n}{n-2}}$ resolvent estimates for…

We prove resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent. Our proof only uses known bounds for the Hadamard parametrix.

We obtain a complete characterization of $L^p-L^q$ Carleman estimates with weight $e^{v\cdot x}$ for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig--Ruiz--Sogge. Consequently, we…

We prove uniform $L^p$ resolvent estimates for the stationary damped wave operator. The uniform $L^p$ resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos…

We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schr\"odinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we…

It is well known that uniform resolvent estimates imply spectral cluster estimates. We show that the converse is also true in some cases. In particular, the universal spectral cluster estimates of Sogge \cite{MR930395} for the…

In this paper we continue the study on the resolvent estimates of the Laplace-Beltrami operator $\Delta_g$ on a compact manifolds $M$ with dimension $n\geq3$. On the Sobolev line $1/p-1/q=2/n$ we can prove that the resolvent…

We prove $L^p-L^{p^\prime}$ boundedness of spectral projections and the resolvent of the Laplace-Beltrami operator on Damek-Ricci spaces with the explicit norms in terms of the spectral parameter. To prove these results we established…

In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds…

In this paper we are concerned with resolvent estimates for the Laplacian $\Delta$ in Euclidean spaces. Uniform resolvent estimates for $\Delta$ were shown by Kenig, Ruiz and Sogge \cite{KRS} who established rather a complete description of…

We prove resolvent estimates in the Euclidean setting for Schr\"{o}dinger operators with potentials in Lebesgue spaces: $-\Delta+V$. The $(L^{2}, L^{p})$ estimates were already obtained by Blair-Sire-Sogge, but we extend their result to…

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…

In this paper, we consider $L^p$- estimate for a class of oscillatory integral operators satisfying the Carleson-Sj\"olin conditions with further convex and straight assumptions. As applications, the multiplier problem related to a general…

We consider restriction analogues on hypersurfaces of the uniform Sobolev inequalities in Kenig, Ruiz, and Sogge and the resolvent estimates in Dos Santos Ferreira, Kenig, and Salo.

We extend the $L^p$-theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis, allied to new ideas that exploit the radial symmetry of this operator. We are then able…

We prove that on a compact Riemannian manifold, resolvent bounds for the Laplace--Beltrami operator imply observability, and thus controllability, for the Schr\"odinger propagator from time sets of positive Lebesgue measure. Applications…

Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the eigenvalues and eigenfunctions of the Laplace-Beltrami…

Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number.…