Related papers: Properties of Sequential Products
We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…
Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments there exist time-dependent covariates that may be posttreatment variables of the earlier…
In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of…
It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential…
Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property of extended stability, which allows…
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…
Following the works of Furstenberg and Glasner on stationary means, we strengthen and extend in this paper some recent results by Di Nasso, Goldbring, Jin, Leth, Lupini and Mahlburg on piecewise syndeticity of product sets in countable…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
With a view to quantum foundations, we define the concepts of an empirical model (a probabilistic model describing measurements and outcomes), a hidden-variable model (an empirical model augmented by unobserved variables), and various…
We study partial derivatives on the product of two metric measure structures, in particular in connection with calculus via modules as proposed by the first named author. Our main results are 1) The extension to this non-smooth framework of…
The theory of uniform approximation of real numbers motivates the study of products of consecutive partial quotients in regular continued fractions. For any non-decreasing positive function $\varphi:\mathbb{N}\to [2,\infty)$, we determine…
We present natural (invariant) definite and indefinite scalar products on the N=1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical…
Measures with values in the set of sesquilinear forms on a subspace of a Hilbert space are of interest in quantum mechanics, since they can be interpreted as observables with only a restricted set of possible measurement preparations. In…
We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of…
Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the…
We consider skew-products with concave interval fiber maps over a certain subshift obtained as the projection of orbits staying in a given region. It generates a new type of (essentially) coded shift. The fiber maps have expanding and…
For a self-adjoint unbounded operator D on a Hilbert space H, a bounded operator y on H and some complex Borel functions g(t) we establish inequalities of the type ||[g(D),y]|| \leq A|||y|| + B||[D,y]|| + ...+ X|[D, [D,...[D, y]...]]||. The…