Related papers: Spectral enclosures for a class of block operator …
We study the operators in the large $N$ tensor models, focusing mostly on the fermionic quantum mechanics with $O(N)^3$ symmetry which may be either global or gauged. In the model with global symmetry we study the spectra of bilinear…
M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices…
In this paper we discuss the problem of decomposition for unbounded $2\times 2$ operator matrices by a pair of complementary invariant graph subspaces. Under mild additional assumptions, we show that such a pair of subspaces decomposes the…
We confirm rigorously the conjecture, based on numerical and asymptotic evidence, that all the eigenvalues of a certain non-self-adjoint operator are real.
Results about angles between Haagerup--Schultz projections for DT-operators whose measures have atoms are proved, which in some cases imply that such operators are non-spectral. Several examples are considered.
We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
In the smooth scattering theory framework, we consider a pair of self-adjoint operators $H_0$, $H$ and discuss the spectral projections of these operators corresponding to the interval $(-\infty,\lambda)$. The purpose of the paper is to…
We extend the concept of Lifshits--Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Our main result is the following. Let…
The Jacobi matrices with bounded elements whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum are considered. A new type of spectral data, which are analogous for…
This paper focuses on the spectral properties of a bounded self-adjoint operator in $L_2(\mathds R^d)$ being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential…
Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to…
We develop an abstract method to identify spectral points of definite type in the spectrum of the operator $T_1\otimes I_2 + I_1\otimes T_2$. The method is applicable in particular for non-self-adjoint waveguide type operators with…
On the half line $[0,\infty)$ we study first order differential operators of the form $B 1/i d/(dx) + Q(x)$, where $B:=\mat{B_1}{0}{0}{-B_2}$, $B_1,B_2\in M(n,\C)$ are self--adjoint positive definite matrices and $Q:\R_+\to M(2n,\C)$,…
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being self-adjoint, and another being non-self-adjoint.…
In this paper we consider 0-th order pseudodifferential operators on the circle. We show that inside any interval disjoint from critical values of the principal symbol, the spectrum is absolutely continuous with possibly finitely many…
We show how the spectrum of normal discrete short-range infinite-volume operators can be approximated with two-sided error control using only data from finite-sized local patches. As a corollary, we prove the computability of the spectrum…