Related papers: Spatio-spectral limiting on hypercubes: eigenspace…

A spectrally isolated quartet can admit a local two-qubit description at each point in parameter space and still acquire a loop holonomy outside the local subgroup $\mathrm{U}(2)\otimes\mathrm{U}(2)$. We study this question in three…

For a class of non-selfadjoint semiclassical operators in dimension one, we get a complete asymptotic description of all eigenvalues near a critical value of the leading symbol of the operator on the boundary of the pseudospectrum.

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…

In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…

We study the gap (= "projection norm" = "graph distance") topology of the space of (not necessarily bounded) self--adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…

Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a…

How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former question is studied in spectral geometry, and the latter is a…

We study the discrete spectrum of the two-particle Schr\"odinger operator $\hat H_{\mu\lambda}(K),$ $K\in\mathbb{T}^2,$ associated to the Bose-Hubbard Hamiltonian $\hat {\mathbb H}_{\mu\lambda}$ of a system of two identical bosons…

In this letter, we study how the spectrum of pseudo-Hermitian systems is influenced by the ambiguity in the choice of the pseudo-metric operator. In particular, we analyze the case when different parameter-independent choices of…

We consider pseudodifferential operators on functions on $\R^{n+1}$ which commute with the Euler operator, and can thus be restricted to spaces of functions homogeneous of some given degree. Their symbols can be regarded as functions on a…

This article is devoted to analytic (in the sense of Boutet de Monvel-Sj\"ostrand) estimates in $\hbar$, of the Bohr-Sommerfeld expansion of the eigenvalues of self-adjoint pseudodifferential operators acting on $L^2(R)$ in the regular…

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…

In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. The lower estimates of the first non-trivial Neumann eigenvalues of the…

Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…

The tunneling spectrum of an inhomogeneously doped extended Hubbard model is calculated at the mean field level. Self-consistent solutions admit both superconducting and antiferromagnetic order, which coexist inhomogeneously because of…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of $A$ decomposes,…