Related papers: Bounded Power Series on the Real Line
Possible forms of obstructed atomic limits in quasi-one-dimensional systems are studied using line group symmetry. This is accomplished by revisiting the standard theory with an emphasis on its group-theoretical background, synthesizing the…
We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description…
This paper catalogues a variety of examples concerning a type of function of a $p$-adic integer variable defined by a formal series expression we have dubbed "$\mathcal{F}$-series". These series exhibit a new, previously undocumented form…
We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.
We obtain some necessary and sufficient conditions for the boundedness of a family of positive operators defined on symmetric cones, we then deduce off-diagonal boundedness of associated Bergman-type operators in tube domains over symmetric…
We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
By a bounded backward sequence of the operator $T$ we mean a bounded sequence $\{x_n\}$ satisfying $Tx_{n+1}=x_n$. In \cite{Pa} we have characterized contractions with strongly stable nonunitary part in terms of bounded backward sequences.…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
We review recent progress in the study of line defects in three-dimensional Chern-Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects supporting a topological sector of the…
We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
Formal power series products appear in nonlinear control theory when systems modeled by Chen-Fliess series are interconnected to form new systems. In fields like adaptive control and learning systems, the coefficients of these formal power…
Let $X,Y,Z$ and $W$ be normed spaces and $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear mapping. In this Article, we define the topological centers for bounded tri-linear mapping and we invistagate thier properties. We…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…