Related papers: A Fredholm Determinant Identity and the Convergenc…
This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty…
After recalling a fundamental identity relating traces and modified Fredholm determinants, we apply it to a class of half-line Schr\"odinger operators $(- d^2/dx^2) + q$ on $(0,\infty)$ with purely discrete spectra. Roughly speaking, the…
In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
In this article we provide with combinatorial proofs of some recent identities due to Sury and McLaughlin. We show that, the solution of a general linear recurrence with constant coefficients can be interpreted as a determinant of a matrix.…
We give a simple algebraic derivation of a useful determinantal identity for multilevel systems such as random matrix chains and finite determinantal point processes, with applications to the calculation of point correlators, gap…
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…
We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are…
The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on $\Z^n\times \mathbb{T}^n$ are proved to coincide and the domain is given in terms of a Sobolev space. Ellipticity and Fredholmness are…
Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections…
A pointed convex cone naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an…
We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context of the Quantum Hall Effect.
We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset ${\Bbb Z}_+^d$ and the graph of its finite ideals, multidimensional Young tableaux;…
Let $\Gamma$ be a compact group acting on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical pseudodifferential operator acting between sections of two equivariant vector bundles $E_i \to M$,…
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
We study the essential spectrum and Fredholm properties of integral and pseudodiferential operators associated to (maybe non-commutative) locally compact groups G. The techniques involve crossed product C*-algebras. We extend previous…
We prove novel results on interpolation of Fredholm operators including an abstract factorization theorem. The main result of this paper provides sufficient conditions on the parameters $\theta \in (0,1)$ and $q\in \lbrack 1,\infty ]$ under…
We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…
This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…