Related papers: Sums and averages

These informal notes deal with a number of questions related to sums and integrals in analysis.

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

This short note contains elementary evaluations of some Euler sums.

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

These informal notes deal with some topics related to analysis on metric spaces.

These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

Informal seminar notes explaining the ideas in math.DS/0411344 and math.DS/0411345.

This article gives a brief survey of the theory and applications of anomalies.

We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).

This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…