Related papers: Potpourri, 5
We study functions which are the pointwise limit of a sequence of holomorphic functions. In one complex variable this is a classical topic, though we offer some new points of view and new results. Some novel results for solutions of…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
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…
We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
This book is an account of certain topics in general and algebraic topology. Instead of laying out a synopsis of each chapter, here is a sample of some of what is taken up: 1) Nilpotency and its role in homotopy theory. 2) Bousfield's…
We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.
Let $\pi$ be a cuspidal automorphic representation of a general linear group over the rational numbers. We establish a subconvex bound for the standard $L$-function of $\pi$ in the $t$-aspect. More generally, we address the spectral aspect…
Mathematical conception of infinite quantities forms a cornerstone of many disciplines of modern mathematics --- from differential calculus to set theory. In fact, it could be argued that the most significant revolutions in mathematics in…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
Numerical functions, which characterize Dynkin schemes, Coxeter graphs and tame marked quivers, are considered.
Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…
We discuss some basic properties of the Sibony functions and pseudometrics.
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
Pippenger's Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set $A$ and taking values in a possibly different set $B$, where any…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
This paper is a direct continuation of the paper arXiv:2401.00053. By this reason neither introductory part of the paper nor the list of references are not duplicated. However for the reader convenience, the formulas from the first paper…
In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…
An explicit C++ library is provided which deals with Zernike Functions over the unit circle as the main subject. The implementation includes basic means to evaluate the functions at points inside the unit circle and to convert the radial…