Related papers: On certain maps defined by infinite sums
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
These are some brief notes on the translation from Razborov's recently-developed notion of flag algebra into the lexicon of functions and measures on certain abstract Cantor spaces (totally disconnected compact metric spaces).
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
In this paper we look at the topological type of algebraic sum of achievement sets. We show that there is a Cantorval such that the algebraic sum of its $k$ copies is still a Cantorval for any $k \in \mathbb{N}$. We also prove that for any…
The input and output algebras of an infinite qubit system and their representations are described.
In this paper we investigate the connections between the several different extensions of the concept of absolutely summing operators.
It is argued that every measurement is made in a certain scale. The scale in which present measuments are made is called present scale which gives present knowledge. Quantities at the limits to present measurement may be observables in…
We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…
We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are $*$-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main…
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
We show that the possible Cantor-Bendixson ranks of countable SFTs are exactly the finite ordinals and ordinals of the form $\lambda + 3$, where $\lambda$ is a computable ordinal. This result was claimed by the author in his PhD…
We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are…
This study describes such a situation that a Cantor set emerges as a result of the exploration of sufficient conditions for the property which is generalized from fundamental chaotic maps, and the Cantor set even guarantees infinitely many…
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions, is strongly bounded.
This paper provides an alternative description for the fixed points of the fractal operator associated with a mixed possibly infinite iterated function system via a canonical projection type function. Some visual aspects of our results are…
We show that every isometric action on a Cantor set is conjugate to an inverse limit of actions on finite sets; and that every isometric action by a finitely generated amenable group is residually finite.
A set of functions is defined which is indexed by a positive integer $n$ and partitions of integers. The case $n=1$ reproduces the standard Schur polynomials. These functions are seen to arise naturally as a determinant of an action on the…
In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an…
This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain…