Related papers: Summable families in tempered distribution spaces
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
We formulate an abstract notion of equidistribution for families of $\lambda$-probability spaces parameterized by admissible $\mathbb{Z}$-sets. Under the assumption of equidistribution, we show that the $\sigma$-moment generating functions…
It is shown that a family of distributions on the complex space is characterized as the only family such that the orbit of one distribution under a certain group of transformations on the complex space is the same as that under the group of…
A definable set $X$ in the first-order language of rings defines a family of random vectors: for each finite field $\mathbb{F}_q$, let the distribution be supported and uniform on the $\mathbb{F}_q$-rational points of $X$. We employ results…
We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…
In this paper we provide necessary and sufficient conditions for the existence of the Kurzweil, McShane and Riemann product integrals of step mappings with well-ordered steps, and for right regulated mappings with values in Banach algebras.…
The aim of this paper is twofold. Firstly, we give easy-to-handle criteria to determine whether a given family of subsets of a vector space is a neighbourhood basis of the origin for a complete vector topology. Then, we apply these criteria…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…
The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of "truth values"), via an appropriate distributive law…
The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…
This paper presents computational methods for families of linear systems depending on a parameter. Such a family is called ensemble controllable if for any family of parameter-dependent target states and any neighborhood of it there is a…
This article is a study on the summability of random Fourier--Jacobi series of some functions in different spaces. We consider the random series $ \sum_{n=0}^\infty a_nA_n(\omega)p_n^{(\gamma,\delta)}(y), $ where…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the…