Related papers: Analytic Continuation of Resolvent Kernels on nonc…

Let $X=G/K$ be a Riemannian symmetric space of the noncompact type and restricted root system $BC_2$ or $C_2$ (except $G=SO_0(p,2)$ with $p>2$ odd). The analysis of the meromorphic continuation of the resolvent of the Laplacian of $X$ is…

Let $(M,g)$ be a globally symmetric space of noncompact type, of arbitrary rank, and $\Delta$ its Laplacian. We prove the existence of a meromorphic continuation of the resolvent $(\Delta-\ev)^{-1}$ across the continuous spectrum to a…

We relate resolvent and scattering kernels for the Laplace operator on Riemannian symmetric spaces of rank one via boundary values in the sense of Kashiwara-Oshima. From this, we derive that the poles of the corresponding meromorphic…

Let $X=X_1 \times X_2$ be a direct product of two rank-one Riemannian symmetric spaces of the noncompact type. We show that when at least one of the two spaces is isomorphic to a real hyperbolic space of odd dimension, the resolvent of the…

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is…

We show that the resolvent of the Laplacian on asymptotically hyperbolic spaces extends meromorphically with finite rank poles to the complex plane if and only if the metric is `even' (in a sense). If it is not even, there exist some cases…

Let $X=G/H$ be a reductive homogeneous space with $H$ noncompact, endowed with a $G$-invariant pseudo-Riemannian structure. Let $L$ be a reductive subgroup of $G$ acting properly on $X$ and $\Gamma$ a torsion-free discrete subgroup of $L$.…

The heat kernel or Bargmann-Segal transform on a noncompact Riemannian symmetric space X=G/K maps a square integrable function on X to a holomorphic function on the complex crown. In this article we determine the range of this transform.

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work we…

Let G/K be a non-compact, rank-one, Riemannian symmetric space and let G^C be the universal complexification of G. We prove that a holomorphically separable, G-equivariant Riemann domain over G^C / K^C is necessarily univalent, provided…

For a compact homogeneous space $G/K$, we study the problem of existence of $G$-invariant Riemannian metrics such that each eigenspace of the Laplacian is a real irreducible representation of $G$. We prove that the normal metric of a…

In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators,…

On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an…

We consider the discrete Laplacian on $\mathbb Z^d$, and compute asymptotic expansions of its resolvent around thresholds embedded in continuous spectrum as well as those at end points. We prove that the resolvent has a square-root…

For $n$ a nonnegative integer, we consider the $n$-Laplacian $\Delta_n$ acting on the space of $n$-differentials on a confinite Riemann surface $X$ which has ramification points. The trace formula for the resolvent kernel is developed along…

We show that the resolvent of the Laplacian on SL(3,$\mathbb{R}$)/SO(3) can be lifted to a meromorphic function on a Riemann surface which is a branched covering of $\mathbb{C}$. The poles of this function are called the resonances of the…

We investigate the nonlinear holomorphic supersymmetry for quantum-mechanical systems on Riemann surfaces subjected to an external magnetic field. The realization is shown to be possible only for Riemann surfaces with constant curvature…

Let $K\backslash G$ be an irreducible Hermitian symmetric space of noncompact type and $\Gamma \,\subset\, G$ a closed torsionfree discrete subgroup. Let $X$ be a compact K\"ahler manifold and $\rho\, :\, \pi_1(X, x_0)\,\longrightarrow\,…

On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ be the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by…