Related papers: The weak n-inner product space

In this paper, we introduce the concept of inner product on weak hypervector spaces and prove some results about them.

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.

It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the…

It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.

In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.

We introduce a n-term quadrature to integrate inner products of n functions, as opposed to a Gaussian quadrature to integrate 2n functions. We will characterize and provide computational tools to construct the inner product quadrature, and…

We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

We consider $p$-weak differentiable structures that were recently introduced by the first and last named authors, and prove that the product of $p$-weak charts is a $p$-weak chart. This implies that the product of two spaces with a $p$-weak…

This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…

A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.

We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak…

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories…

We study the difference between internal categories and internal groupoids in terms of generalised Mal'tsev properties---the weak Mal'tsev property on the one hand, and $n$-permutability on the other. In the first part of the article we…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

In this paper, we extend the definition of hyperinner product defined on weak hypervector spaces with a hyperoperation scalar product to weak hypervector spaces with the hyperoperations sum and scalar products.

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and…

In this paper is defined an $n$-inner product of type $\langle {\bf a}_1,\cdots ,{\bf a}_n\vert {\bf b}_1\cdots {\bf b}_n\rangle $ where ${\bf a}_1,\cdots ,{\bf a}_n$, ${\bf b}_1, \cdots ,{\bf b}_n$ are vectors from a vector space $V$. This…

We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…