Related papers: Notes on the sin2\Theta\ theorem

The Ray-Singer isospectral theorem (1971) is applied to a general spectral function for Laplacians of twisted p-forms (say) on homogeneous Clifford-Klein factors of the three-sphere. The inducing formulae necessary to express any spectral…

A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with…

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…

We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the lower half of the complex plane. We find several application of this fact in scattering by obstacles with impedance boundary conditions. In particular, we find an…

Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous…

Under certain assumptions (including $d\ge 2)$ we prove that the spectrum of a scalar operator in $\mathscr{L}^2(\mathbb{R}^d)$ \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*} covers interval…

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…

We review the spectral and the scattering theory for the Aharonov-Bohm model on R^2. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high and at low energy of the scattering operator are…

In this work we introduce a new measure for the dispersion of the spectral scale of a Hermitian (self-adjoint) operator acting on a separable infinite dimensional Hilbert space that we call spectral spread. Then, we obtain some…

We derive the anomalous transformation law of the quantum stress tensor for a 2D massless scalar field coupled to an external dilaton. This provides a generalization of the Virasoro anomaly which turns out to be consistent with the trace…

We apply Schmidt's Subspace Theorem to establish Arithmetic General Theorems for projective varieties over number and function fields. Our first result extends an analogous result of M. Ru and P. Vojta. One aspect to its proof makes use of…

In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski-Sitarz-Zalecki type theorems associated with the spectral…

Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…

We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form \[ \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx} + q\right) \] and prove perturbation results and…

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…

This paper presents the perturbation theory for the double--sine--Gordon equation. We received the system of differential equations that shows the soliton parameters modification under perturbation's influence. In particular case…

Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the…

Let $M$ be a stratum of a compact stratified space $A$. It is equipped with a general adapted metric $g$, which is slightly more general than the adapted metrics of Nagase and Brasselet-Hector-Saralegi. In particular, $g$ has a general…

We analyse an operator arising in the description of singular solutions to the two-dimensional Keller-Segel problem. It corresponds to the linearised operator in parabolic self-similar variables, close to a concentrated stationary state.…