相关论文: The Pseudospectrum of Systems of Semiclassical Ope…
We obtain dynamical lower bounds for some self-adjoint operators with pure point spectrum in terms of the spacing properties of their eigenvalues. In particular, it is shown that for systems with thick point spectrum, typically in Baire's…
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…
We define a class of pseudo-ergodic non-self-adjoint Schr\"odinger operators acting in spaces $l^2(X)$ and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson…
Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
The spectral behavior of the difference between the resolvents of two realizations $\tilde A_1$ and $\tilde A_2$ of a second-order strongly elliptic symmetric differential operator $A$, defined by different Robin conditions $\nu…
We prove, under some generic assumptions, that the semiclassical spectrum modulo O(h^2) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the…
Despite considerable progress during the last decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg…
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…
Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…
The origin of pseudospin symmetry and its broken in real nuclei are discussed in the relativistic mean field theory. In the exact pseudospin symmetry, even the usual intruder orbits have degenerate partners. In real nuclei, pseudospin…
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We consider the operator $${\cal H} = {\cal H}' -\frac{\partial^2\ }{\partial x_d^2} \quad\text{on}\quad\omega\times\mathbb{R}$$ subject to the Dirichlet or Robin condition, where a domain $\omega\subseteq\mathbb{R}^{d-1}$ is bounded or…
In this work, we wish to address the question -- whether the quasi-normal modes, the characteristic frequencies associated with perturbed black hole spacetimes, central to the stability of these black holes, are themselves stable. Though…
We shall study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol…
We consider a nonlinear evolution problem with an asymptotic parameter and construct examples in which the linearized operator has spectrum uniformly bounded away from Re z >= 0 (that is, the problem is spectrally stable), yet the nonlinear…
In this paper we prove local solvability of quasilinear pseudodifferential operators which has homogeneous principal symbol of real principal type. This generalizes Theorem A.1 in arXiv:2403.19054, which treats the case of quasilinear…