Related papers: Mixing property and pseudo random sequences

We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…

We describe the general qualitative behaviour of the resolvent norm for a very wide class of non-self-adjoint Schroedinger operators in the semi-classical regime, as the spectral parameter varies over the complex plane.

For families of magnetic pseudodifferential operators defined by symbols and magnetic fields depending continuously on a real parameter $\epsilon$, we show that the corresponding family of spectra also varies continuously with $\epsilon$.

The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes.…

By using quasi--derivatives, we develop a Fourier method for studying the spectral properties of one dimensional Schr\"odinger operators with periodic singular potentials.

We show that the use of the main characteristics of the circle map leads naturally to establish a few statements on primes and pseudoprimes. In this way a Fermat's theorem on primes and some interesting properties of pseudoprimes are…

We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral…

We survey results concerning the spectral properties of limit-periodic operators. The main focus is on discrete one-dimensional Schr\"odinger operators, but other classes of operators, such as Jacobi and CMV matrices, continuum…

We characterize the space of the so-called planar mixed automorphic forms of type $(\nu,\mu)$ with respect to an equivariant pair $(\rho,\tau)$ as the image of the usual automorphic forms by an appropriate transform and we investigate some…

We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove…

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

We derive a generalization of the Perron-Frobenius theorem to time-varying row-stochastic matrices as follows: using Kolmogorov's concept of absolute probability sequences, which are time-varying analogs of principal eigenvectors, we…

Mixing-demixing transitions in one-dimensional mixtures of fermions and bosons are numerically investigated. With Monte Carlo simulations, we searched the transitions by changing various parameters such as number densities of each…

The pseudo--spectral decomposition of an $N$--particle antisymmetric 1--body positive--semidefinite operator that corresponds to the canonical convex decomposition into the extreme elements of the dual cone of the set of fermion…

In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…

We find the singular transformation between the electron operator and the pseudoparticle operators for the Hubbard chain. We generalize the concept of quasiparticle to one-dimensional electronic systems which in 1D refers to…

We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner…

We show that the occurrence of approximate pseudo-spin symmetry in nuclei is connected with certain similarities in the relativistic single-nucleon wave functions of the corresponding pseudo-spin doublets. We perform a case study in which…

We give a brief survey of recent results concerning almost diagonalization of pseudodifferential operators via Gabor frames. Moreover, we show new connections between symbols with Gevrey, analytic or ultra-analityc regularity and…