相关论文: The spectra of the spherical and euclidean triangl…

We show that non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum. This extends our previous result, which was only concerned with the Neumann Laplace spectrum.

In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…

Matrix elements of irreducible representations of the Lorentz group are calculated on the basis of complex angular momentum. It is shown that Laplace-Beltrami operators, defined in this basis, give rise to Fuchsian differential equations.…

Of the two main objectives we pursue in this paper, the first one consists in the studying operators of the form $(\partial_t-i\triangle_{\Gamma})^{\alpha},\,\,\alpha=1/2,-1/2,-1,\ldots,$ where $\triangle_{\Gamma}$ is the Laplace-Beltrami…

We consider the spectrum of the Laplace operator acting on $\mathcal{L}^p$ over a conformally compact manifold for $1 \leq p \leq \infty$. We prove that for $p \neq 2$ this spectrum always contains an open region of the complex plane. We…

We obtain an asymptotic formula for the spectrum distribution function of the Laplace operator on a compact Riemannian Sol-manifold in the adiabatic limit determined by a one-dimensional foliation defined by the orbits of a left-invariant…

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace-Beltrami operator on functions and the Laplacian on powers of the cotangent bundle.…

We compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the Hardy and weighted Bergman spaces of the upper half-plane. We are also able to extend the results to weighted Dirichlet spaces…

We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…

We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…

We prove a trace formula for three-dimensional spherically symmetric Riemannian manifolds with boundary which satisfy the Herglotz condition: The wave trace is singular precisely at the length spectrum of periodic broken rays. In…

For Laplace-Beltrami operators associated to metrics which are long range perturbations of the flat one, we prove estimates for powers of the resolvent as the spectral parameter goes to zero. We also discuss applications to the local energy…

In the first part of this Chapter, we discuss the role of spectral observables, describing possible ways to build them from discretizations of the Laplace--Beltrami operator on triangulations, and how to extract useful geometric…

We establish an explicit expression for the smallest non-zero eigenvalue of the Laplace--Beltrami operator on every homogeneous metric on the 3-sphere, or equivalently, on SU(2) endowed with left-invariant metric. For the subfamily of…

We prove a formula for the spectrum of the Laplace-Beltrami operator on functions for compact naturally reductive homogeneous spaces in terms of eigenvalues of a generalized Casimir operator and spherical representations. We apply this…

Let $\mathscr{L}$ be a smooth second-order real differential operator in divergence form on a manifold of dimension $n$. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of…

The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schr\"odinger operator has a finite or infinite number of the discrete pectrum. In…

We present a few subjects from physics that have one in common: the spectral resolution of the Laplacian.

In this article, we study the Fu\v{c}ik spectrum of fractional Laplace operator which is defined as the set of all $(\al,\ba)\in \mb R^2$ such that \begin{equation*} \quad \left. \begin{array}{lr} \quad (-\De)^s u = \al u^{+} - \ba u^{-} \;…

This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit…