相关论文: Distances between composition operators
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact…
In this short article, for any matrix $X\in\mathbb{R}^{n\times m}$ the proximity operator of two induced norms $ \|X\|_1 $ and $ \|X\|_{\infty}$ are derived. Although no close form expression is obtained, an algorithmic procedure is…
The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…
We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of…
Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is…
We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
For a tuple of operators $\boldsymbol{A}= (A_1, \ldots, A_d)$, $\text{dist}(\boldsymbol{A}, \mathbb C^d \boldsymbol{I})$ is defined as $\min\limits_{\boldsymbol{z} \in \mathbb C^d} \|\boldsymbol{A-zI}\|$ and $\text{var}_x (\boldsymbol{A})$…
The aim of this paper is to discuss the characterizations of the composition operators on Orlicz-Lorentz space to have finite ascent (or descent).
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.
We study the decay of approximation numbers of compact composition operators on the Dirichlet space. We give upper and lower bounds for these numbers. In particular, we improve on a result of O. El-Fallah, K. Kellay, M. Shabankhah and A.…
In this paper, the order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights are characterized. Specially, we estimate the essential norm of these operators on weighted…
We give a simple polynomial-time approximation algorithm for the total variation distance between two product distributions.
Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…