Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described linear Koopman operator. This letter describes how operator used generate approximate linear, bilinear, and nonlinear model realizations from data, argues in favor bilinear for characterizing with unknown dynamics. Necessary sufficient conditions a...

In this paper, we consider the class of infinite-dimensional discrete-time linear systems with multiplicative random disturbances (i.e. with the state multiplied by a random sequence), also known as stochastic bilinear systems. We formulate and solve the quadratic optimal-control problem for this class of systems subject to an arbitrary additive stochastic £2 input disturbance. Under assumption...

We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also cons...

Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1]. The main object of this paper is to present a further generalization of the extended fractional derivative operator and apply the generalized extended fractional derivative operator to derive lin...

We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also cons...

In this article, we consider an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group Hn. We completely characterize exponents α,β γ such that is bounded from Lp(Hn,|x|αp)×Lq(Hn,|x|βq) to Lr(Hn,|x|−γr). Also, analogous sharp results are obtained Euclidean space.

We outline the super-resolution reconstruction problem posed as a maximization of probability. We then introduce an interpolation method based on polygonal pixel overlap, express it as a linear operator, and use it to improve reconstruction. Polygon interpolation outperforms the simpler bilinear interpolation operator and, unlike Gaussian modeling of pixels, requires no parameter estimation. A ...

The term paraproduct is nowadays used rather loosely in the literature to indicate a bilinear operator that, although noncommutative, is somehow better behaved than the usual product of functions. Paraproducts emerged in J.-M. Bony’s theory of paradifferential operators [1], which stands as a milestone on the road beyond pseudodifferential operators pioneered by R. R. Coifman and Y. Meyer in [3...

We first prove an adiabatic limit formula for the rf-invariant of aDirac operator, generalizing the recent work of J.-M. Bismut and J. Cheeger.An essential part of the proof is the study of the spectrum of the Dirac op-erator in the adiabatic limit. A new contribution arises in the adiabatic limitformula, in the form of a global term coming from the (asymptotically) verysmal...