Related papers: Erdelyi-Kober Fractional Integral Operators from a…
We study here the effects of a time-dependent second order perturbation to a degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either local or non-local. More precisely, we establish that some estimates, such as the…
We study the level statistics for two classes of 1-dimensional random Schr\"odinger operators : (1) for operators whose coupling constants decay as the system size becomes large, and (2) for operators with critically decaying random…
Let $D(s)$ be a fractional derivation of order $s$. For a real $p\ne 0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p) D(s) A(p)^{-1}=D(p s)$ for all $s$. The kernel of the operator $A(p)$ is…
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
We consider diffusive systems, regarded as input/output systems with a kernel given as the Fourier--Borel transform of a measure in the left half-plane. Associated with these are a family of weighted Hankel integral operators, and we…
This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We consider the analysis of probability distributions through their associated covariance operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy and relative entropy of these operators are intimately related…
We establish a necessary density criterion for the identifiability of time-frequency structured classes of Hilbert-Schmidt operators. The density condition is based on the density criterion for Gabor frames and Riesz bases in the space of…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
We introduce a formal $\hbar$-differential operator $\Delta$ that generates higher Koszul brackets on the algebra of (pseudo)differential forms on a $P_{\infty}$-manifold. Such an operator was first mentioned by Khudaverdian and Voronov in…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
In the geometric approach to define complexity, operator complexity is defined as the distance on the operator space. In this paper, based on the analogy with the circuit complexity, the operator size is adopted as the metric of the…
We study a family of fractional integral operators defined in $\mathbb{R}^3$ whose kernels are distributions associated with Zygmund dilations: $(x_1, x_2, x_3) \rightarrow (\delta_1 x_1, \delta_2 x_2, \delta_1\delta_2 x_3)$ for…
We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
We aim to give a self-contained and detailed yet simplified account of the foundations of the theory of double operator integrals, in order to provide an accessible entry point to the theory. We make two new contributions to these…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
In the paper, the transition probability density of isotropic $\alpha$-stable stochastic process in a finite dimensional Euclidean space is considered. The results of applying pseudo differential operators with respect spatial variables to…