EXPOSITIO

A home for expository scholarship

Expositio is a repository for expository papers in a wide range of academic disciplines, supporting preprints, revisions, optional peer review, saved papers, and overlay journals.

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What is Expositio?

A public repository for expository academic papers, with an integrated scholarly record.

Expositio is a place to read and cite expository work. Papers are published as stable, citable records, while remaining connected to later versions, editorial decisions, and related context.

Some papers are early drafts; others have been peer reviewed or formally published. Each paper remains readable on its own, while preserving the history behind it.

The result is both a reading room and a record: a place to browse by field, read papers in stable form, and follow their development over time.

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Abstract harmonic analysis

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Mathematics Abstract harmonic analysis Abstract harmonic analysis
Domain: Mathematics × Branch: Abstract harmonic analysis × Branch: Abstract harmonic analysis ×

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Expositio paper

Infinite Series Through Fourier Analysis

Aleksei Lopatin

Preprint
v1

In this paper, we will introduce Fourier Series through the Orthogonality Relations from which we consider Parseval's Theorem. Then, we wish to extend the concept of Fourier Series of aperiodic functions, specifically showing the Fourier Transform. The usage of the Fourier Trans…

Mathematics / Abstract harmonic analysis
Mathematics > Abstract harmonic analysis > Other transforms and operators of Fourier type Primary

Expositio paper

The Algebraic Structure Underlying Fourier Analysis

Siddharth Kothari

Preprint
v1

In this paper, we begin with the concept of a projection in the familiar vector space R^n, and then extend it to an arbitrary inner product space. This foundational idea enables us to compute a line of best fit, approximate functions using polynomials, and decompose a function i…

Mathematics / Abstract harmonic analysis Mathematics / Group theory and generalizations
Mathematics > Abstract harmonic analysis > Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups Primary
Mathematics > Group theory and generalizations > Finite abelian groups