Related papers: Spectral theory for bounded banded matrices with p…
We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal…
In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real…
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small constant-depth circuit or formula, then…
We prove an inequality for the spectral norm of matrix valued stochastic integrals. This inequality can be seen either as a non-commutative version of the Burkholder-Davis-Gundy inequality or as an extension of the non-commutative…
We study the topology of real polynomial maps $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates, which we refer to as bicomplex mixed polynomials. We introduce the notion of…
We introduce and initiate the investigation of a general class of 4d, N=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as…
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…
A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…
This paper is concerned with the inverse elastic scattering problem to determine the shape and location of an elastic cavity. By establishing a one-to-one correspondence between the Herglotz wave function and its kernel, we introduce the…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…
We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the…
For a fixed quadratic polynomial $\mathfrak{p}$ in $n$ non-commuting variables, and $n$ independent $N\times N$ complex Ginibre matrices $X_1^N,\dots, X_n^N$, we establish the convergence of the empirical spectral distribution of $P^N…
The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
We give a non-asymptotic bound on the spectral norm of a $d\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\sqrt{\log d}$…
We propose an alternative factorization for the simple harmonic oscillator hamiltonian which includes Mielnik's isospectral factorization as a particular case. This factorization is realized in two non-mutually adjoint operators whose…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
An input pair $(A,B)$ is triangular input normal if and only if $A$ is triangular and $AA^* + BB^* = I_n$, where $I_n$ is theidentity matrix. Input normal pairs generate an orthonormal basis for the impulse response. Every input pair may be…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
A brief review of checking the factorization hypothesis for matrix element of $B^0 - \bar B^0$ mixing within operator product expansion and QCD sum rules is given. Both perturbative and power corrections are considered.