Related papers: Weyl's Law for Arbitrary Archimedean Type

The gauge formulation of Einstein gravity in AdS$_3$ background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is…

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical…

We study self-adjoint extensions of a second order differential operator of Sturm-Liouville type on a graph. We relate self-adjointness of the operator to the existence of non-complete trajectories of the Hamiltonian vector field defined by…

We present an explicit formula for the leading coefficient in the asymptotic expansion of the eigenvalue counting function of the Kohn Laplacian on the unit sphere $\mathbb{S}^{2n-1}$.

In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the…

We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those -highly symmetric -geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of…

In this work we study the asymptotic behavior of the curves of the Fu{\v{c}}{\'{\i}}k spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the…

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme…

For a general class of unitary quantum maps, whose underlying classical phase space is divided into several invariant domains of positive measure, we establish analogues of Weyl's law for the distribution of eigenphases. If the map has one…

For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application, we show in…

The Laplacian of a (weighted) Cayley graph on the Weyl group $W(B_n)$ is a $N\times N$ matrix with $N = 2^n n!$ equal to the order of the group. We show that for a class of (weighted) generating sets, its spectral gap (lowest nontrivial…

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important \qo{Pauli Exclusion Principle} but by the adoption of the complex standard relativistic quantum field…

Employing Br\"udern's and Wooley's new complification method, we establish an asymptotic Hasse principle for the number of solutions to a system of r_3 cubic and r_2 quadratic diagonal forms, when the number of cubic equations is at least…

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive.…

Let $\mathbf{T}$ be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property $$ \textrm{dim} \; \textrm{ker} \; (\mathbf{T}-\boldsymbol\lambda) \ge \textrm{dim} \; \textrm{ker} \; (\mathbf{T} -…

We study the relationship between the arithmetic and the spectrum of the Laplacian for manifolds arising from congruent arithmetic subgroups of SL(1,D), where D is an indefinite quaternion division algebra defined over a number field F. We…

Semiclassical analysis and noncommutative geometry are two pillars of quantum theory. It is only recently that bridges between them have been emerging. In this monograph, we combine various techniques from functional analysis and spectral…

We prove qualitative and quantitative results concerning the asymptotic density in dilates of centered convex bodies of the frequency vectors of orthogonal exponential bases and frames associated to bounded domains in Euclidean space.

The paper is concerned with the Steklov eigenvalue problem on cuboids of arbitrary dimension. We prove a two-term asymptotic formula for the counting function of Steklov eigenvalues on cuboids in dimension d greater or equal to 3. Apart…