Related papers: Riesz operators and some spherical representations…

Let \( P \) and \( Q \) be the quantum-mechanical momentum and position operators on \( L^2(\R) \). Let $\zeta>0.$ We provide estimates for the {\it Riesz means} $\varkappa(\lambda)$ associated with the system of eigenvalues of the operator…

The classical Perron-Frobenius theory asserts that an irreducible matrix $A$ has cyclic peripheral spectrum and its spectral radius $r(A)$ is an eigenvalue corresponding to a positive eigenvector. In Radjavi (1999) and Radjavi and Rosenthal…

We examine unitary and nonunitary representations of the Heisenberg-Weyl Lie algebra $\mathfrak{hw}_n$, with particular emphasis on tensor products of unitary representations and on indecomposable nonunitary representations. In the unitary…

Schur modules give the irreducible polynomial representations of the general linear group $\mathrm{GL}_t$. Viewing the symmetric group $\mathfrak{S}_t$ as a subgroup of $\mathrm{GL}_t$, we may restrict Schur modules to $\mathfrak{S}_t$ and…

We derive a dyadic model operator for the Riesz vector. We show linear upper $L^p$ bounds for $1 < p < \infty$ between this model operator and the Riesz vector, when applied to functions with values in Banach spaces. By an upper bound we…

Liv\v{s}ic theorem asserts that, for Anosov diffeomorphisms/flows, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The transfer function is then Lipschitz. We prove a positive…

We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or…

We construct an explicit intertwining operator $\lcal$ between the Schr\"odinger group $e^{it \frac\Lap2} $ and the geodesic flow $g^t$ on certain Hilbert spaces of symbols on the cotangent bundle $T^* \X$ of a compact hyperbolic surface…

In this paper we continue work in the direction of a characterization of rational period functions on the Hecke groups. We examine the role that Hecke-symmetry of poles plays in this setting, and pay particular attention to non-symmetric…

Consider the Hill operator $L(v) = - d^2/dx^2 + v(x) $ on $[0,\pi]$ with Dirichlet, periodic or antiperiodic boundary conditions; then for large enough $n$ close to $n^2 $ there are one Dirichlet eigenvalue $\mu_n$ and two periodic (if $n$…

New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov and the Landau-Lifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple…

In this paper we consider a large family of graphs of hierarchically hyperbolic groups (HHG) and show that their fundamental groups admit HHG structures. To do that, we will investigate the notion of hierarchical quasi convexity and show…

We consider a reducible unitary representation of Heisenberg-Weyl group in a tensor product of two Hilbert spaces. A non-commutative operator graph generated by this representation is introduced. It is shown that spectral projections of…

In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols…

Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian…

Given a unitary representation of a Lie group $G$ on a Hilbert space $\mathcal{H}$, we develop the theory of $G$-invariant self-adjoint extensions of symmetric operators both using von Neumann's theorem and the theory of quadratic forms. We…

The classic Riesz representation theorem characterizes all linear and increasing functionals on the space $C_{c}(X)$ of continuous compactly supported functions. A geometric version of this result, which characterizes all linear increasing…

A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.

In this article, we investigate the bilinear Riesz means $S^{\alpha }$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{\alpha }$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $ L^{p}$ for $1\leq…

The main mathematical manifestation of the Stark effect in quantum mechanics is the shift and the formation of clusters of eigenvalues when a spherical Hamiltonian is perturbed by lower order terms. Understanding this mechanism turned out…