Related papers: A note on lineability
A general theorem on fibers of singular sets is presented.
For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility…
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…
In this note we associate a sequence of non-negative integers to any convergent series of positive real numbers and study this sequence for the series $\sum_{n \geq 1} n^{-k}$ where $k$ is an integer $\geq 2$.
The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.
The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity.
We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$…
We prove that the multiple summing norm of multilinear operators defined on some $n$-dimensional real or complex vector spaces with the $p$-norm may be written as an integral with respect to stables measures. As an application we show…
In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.
In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
We address the "sums of dilates problem" by looking for non-trivial lower bounds on sumsets of the form $k \cdot X + l \cdot X$, where $k$ and $l$ are non-zero integers and $X$ is a subset of a possibly non-abelian group $G$ (written…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
We investigate some modal operators of necessity and possibility in the context of meet-complemented (not necessarily distributive) lattices. We proceed in stages. We compare our operators with others.
In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete relational model for this calculus.
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
We discuss how countable subadditivity of operators can be derived from subadditivity under mild forms of continuity, and provide examples manifesting such circumstances.
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…