Related papers: Normability of Probabilistic Normed Spaces

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…

We consider the fundamental question of learnability of a hypotheses class in the supervised learning setting and in the general learning setting introduced by Vladimir Vapnik. We survey classic results characterizing learnability in term…

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.

In this article, we generalize the notion of orthogonality as a linear combination of norm derivatives in order to give a novel concept that we refer to as $\rho_{\alpha,\beta}$-orthogonality. Also, we discuss some of its geometric…

We consider questions related to quantizing complex valued functions defined on a locally compact topological group. In the case of bounded functions, we generalize R. Werner's approach to prove the characterization of the associated normal…

Unstable coalgebras over the Steenrod algebra form a natural target category for singular homology with prime field coefficients. The realization problem asks whether an unstable coalgebra is isomorphic to the homology of a topological…

In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.

The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces. We will deduce general criteria by transferring and extending a theorem of Bui,…

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…

The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We…

We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any…

Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…

In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions originally considered by Dales and Davie. For many compact plane sets the classical…

This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…

Nearly three decades from his celebrated result, we study a modern refinement and strengthening of Kopperman's full metrisabilty of all topological spaces. Within this new theory of \emph{V-spaces}, developed by Flagg and Weiss, we…

Some new bounds for Cebysev functional for sequences of vectors in normed linear spaces are pointed out.

In this chapter, we review a principled way of defining and measuring contextuality in systems with deterministic inputs and random outputs, recently proposed and developed in \citep{KujalaDzhafarovLarsson2015,DKL2015FooP}.

We are concerned here with Sobolev-type spaces of vector-valued functions. For an open subset $\Omega\subset\mathbb{R}^N$ and a Banach space $V$, we compare the classical Sobolev space $W^{1,p}(\Omega, V)$ with the so-called…