相关论文: A General Framework for Extending Means to Higher …

Firmly nonexpansive operators arise naturally as resolvents of monotone operators and as generalizations of projections and proximal mappings in convex optimization and fixed point theory. While their iterates are known to converge weakly…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…

Making use of the simple fact that all separable complex Hilbert spaces of given dimension are isomorphic, we show that there are just six basic ways to define generalized coordinate operators in Quantum Mechanics. In each case a…

We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…

In this note, we frst consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the…

In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to…

The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…

Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…

In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…

We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results…