Related papers: Notes on algebras and vector spaces of functions
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological…
Reeb spaces of real-valued functions on manifolds are the spaces of all connected components (contours) of level sets and endowed with the natural quotient topology. They have been fundamental and strong tools in investigating manifolds via…
In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
The paper gives a brief account of the spaces of interval functions defined through the concepts of H-continuity, D-continuity and S-continuity. All three continuity concepts generalize the usual concept of continuity for real (point…
A functional Menger $\cap$-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's compositions of n-place functions and the set-theoretic intersection of functions. We give the abstract…
Some boundedness properties of function spaces (considered as topological groups) are studied.
In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…
By using the space of fuzzy numbers, in e.g. [5] have been considered several complete metric spaces (called here {\bf FN}-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the…
Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…