相关论文: Spectral multiplicity and odd K-theory-II

Two graphs are co-spectral if their respective adjacency matrices have the same multi-set of eigenvalues. A graph is said to be determined by its spectrum if all graphs that are co-spectral with it are isomorphic to it. We consider these…

In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…

A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.

Here, we focus on Anderson type operators over infinite graphs where the randomness acts through higher rank perturbations. We show that for special family of graphs, the operator has non-trivial multiplicity for its pure point spectrum.…

Let A denote the C*algebra of bounded operators on L2(R) generated by: (i) all multiplications a(M) by functions a\in C[-\infty,+\infty], (ii) all multiplications by 2\pi-periodic continuous functions and (iii) all Fourier multipliers…

Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…

We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on…

We construct $S^r$-colored knot Floer homologies and prove that they satisfy categorified recurrence relations. The associated Euler characteristic implies $q$-holonomicity of the corresponding sequence of colored Alexander polynomials, in…

In the present paper our aim is to explore some spectral properties of the family two-particle discrete Schr\"odinger operators $h^{\mathrm{d}}(k)=h^{\mathrm{d}}_0(k)+ \mathbf{v},$ $k\in \T^\mathrm{d},$ on the $\mathrm{d}$ dimensional…

Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts,…

Let $\{A(t)\}_{t \in \mathbb{R}}$ be a path of self-adjoint Fredholm operators in a Hilbert space $\mathcal{H}$, joining endpoints $A_\pm$ as $t \to \pm \infty$. Computing the index of the operator $D_A= (d/d t) + A$ acting in…

We study the Spectral Analysis for a class of bounded linear operators T = D + F in a non Archimedean Hilbert space E, where D is a diagonal linear operator and where F is a finite rank linear operator. In this study of the Spectral…

We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…

This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that…

We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A together with an explicit functor from the category of…

The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings…

We present spectrally disjoint Sidon automorphisms whose tensor squares are isomorphic to a planar shift. Spectra of such automorphisms do not possess the group property. To check the singularity of spectrum, we use polynomial rigidity of…

The main objective of this paper is to systematically develop a spectral and scattering theory for selfadjoint Schr\"odinger operators with $\delta$-interactions supported on closed curves in $\mathbb R^3$. We provide bounds for the number…

Based on our previous studies of the BRST cohomology of the critical N=2 strings, we construct the loop measure and make explicit the role of the spectral flow at arbitrary genus and Chern class, in a holomorphic field basis. The spectral…

The existence and continuity for the Calderon projector of the perturbed odd signature operator on a 3-manifold is established. As an application we give a new proof of a result of Taubes relating the mod 2 spectral flow of a family of…