Related papers: The weak n-inner product space
Through a reformulation of the local limit theorem and law of small numbers, which is obtained by working in the spaces naturally associated to the limiting distributions, we discover a general and abstract framework for the investigation…
We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…
We introduce a weak Gurov-Reshetnyak class and discuss its connections to a weak Muckenhoupt $A_\infty$ condition and a weak reverse H\"older inequality in the setting of metric measure spaces with a doubling measure. A John-Nirenberg type…
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds,…
In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain \Om in Euclidean n-space, k=1,...,n, and proved a weak continuity result with respect to local…
The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…
We study a class of inner functions introduced by Gorkin, Mortini, and Nikolski, and motivated by Banach algebras and functional calculus applications. Answering their question, we produce a singular function that cannot be multiplied into…
Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…
In this paper we introduce the notion of weak 2-positivity and present some examples. We establish some operator Cauchy--Schwarz inequalities involving the geometric mean and give some applications. In particular, we present some operator…
Weak-to-strong generalization (W2SG) has emerged as a promising paradigm for stimulating the capabilities of strong pre-trained models by leveraging supervision from weaker supervisors. To improve the performance of the strong model,…
The weak tensor product was introduced by Snevily as a way to construct new graphs that admit $\alpha$-labelings from a pair of known $\alpha$-graphs. In this article, we show that this product and the application to $\alpha$-labelings can…
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out…
A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…
A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given.
Normalized nonnegative models assign probability distributions to users and random variables to items; see [Stark, 2015]. Rating an item is regarded as sampling the random variable assigned to the item with respect to the distribution…
We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1<p,q<\infty$ be such that $1/p+1/q\geq 1$. Let $X$ (resp., $Y$) be…
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…
In continuation of the paper [3], we discuss various consequences of Hahn-Banach theorem for bounded b-linear functional in linear n-normed space and describe the notion of reflexivity of linear n-normed space with respect to bounded…