Related papers: Sums and averages
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
These notes, associated with a topics course, deal with some special features of summability and supremum norms which are often useful.
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
Some notes and observations on analytic functions defined on an annulus
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
The relation between tempered distributions and measures is analysed and clarified. While this is straightforward for positive measures, it is surprisingly subtle for signed or complex measures.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Certain new inequalities for the sums of factorials are presented.
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
The annotation of textual information is a fundamental activity in Linguistics and Computational Linguistics. This article presents various observations on annotations. It approaches the topic from several angles including Hypertext,…
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
In these introductory lectures we discuss classes of presently known nested sums, associated iterated integrals, and special constants which hierarchically appear in the evaluation of massless and massive Feynman diagrams at higher loops.…
This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…
Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.
This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…
These informal notes briefly discuss various aspects of Cantor sets.
We show that there are short intervals $[x,x+y]$ containing $\gg y^{1/10}$ numbers expressible as the sum of two squares, which is many more than the average when $y=o( (\log{x})^{5/9})$. We obtain similar results for sums of two squares in…