Related papers: On Operator-valued Semicircular Random Variables
We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition" of the solutions to two simpler problems. These Cauchy sub-problems respectively…
We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…
We consider a Sturm-Liouville operator a with integrable potential $q$ on the unit interval $I=[0,1]$. We consider a Schr\"odinger operator with a real compactly supported potential on the half line and on the line, where this potential…
In this paper, we propose a new flexible distribution for data on the three-dimensional torus which we call a trivariate wrapped Cauchy copula. Our trivariate copula has several attractive properties. It has a simple form of density and…
We obtain some $L^2$ results for the Cauchy-Riemann operator on forms that vanish to high order near the singular set of a complex space.
We define and examine certain matrix-valued multiplicative functionals with local Kato potential terms and use probabilistic techniques to prove that the semigroups of the corresponding partial differential operators with matrix-valued…
We introduce and characterize, on the Banach lattice valued continuous function space, multiplication operators generating strongly continuous multiplication operator semigroups. Our characterization is the generalization of known results…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
We address continuous weak linear quantum measurement and argue that it is best understood in terms of statistics of the outcomes of the linear detectors measuring a quantum system, for example, a qubit. We mostly concentrate on a setup…
The abstract Cauchy problem for the distributed order fractional evolution equation in the Caputo and in the Riemann-Liouville sense is studied for operators generating a strongly continuous one-parameter semigroup on a Banach space.…
The quantum analogue of the classical characteristic function for a spin 1/2 assembly is considered and the probability mass function of the random vector associated with the assembly is derived. It is seen that the positive regions of…
Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.
We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in [24] and [12] in this case…
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 generalize the operational quasiprobability involving sequential measurements proposed by Ryu {\em et al.} [Phys. Rev. A {\bf 88}, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate,…
Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…
A quasi-infinitely divisible distribution on $\mathbb{R}^d$ is a probability distribution $\mu$ on $\mathbb{R}^d$ whose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible…
We consider five different abstract Cauchy problems where the operator is of fourth order. For each problem, using semigroups techniques and functional calculus, we study the invertibility and the spectral properties of the fourth order…
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…