Almost Periodic Functions
E486749
Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Almost Periodic Functions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5019711 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Almost Periodic Functions Context triple: [Harald Bohr, hasWork, Almost Periodic Functions]
-
A.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
B.
Du Bois-Reymond function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
E.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Almost Periodic Functions Target entity description: Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
-
A.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
B.
Du Bois-Reymond function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real analysis.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
E.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author | Harald Bohr NERFINISHED ⓘ |
| basedOn | Harald Bohr's earlier papers on almost periodic functions ⓘ |
| centralConcept |
Bohr almost periodic function
ⓘ
Bohr compactification NERFINISHED ⓘ Bohr–Fourier series NERFINISHED ⓘ equivalence of definitions of almost periodicity ⓘ mean value of an almost periodic function ⓘ relative denseness of ε-almost periods ⓘ uniform approximation by trigonometric polynomials ⓘ |
| characterizes |
almost periodic functions via Bohr–Fourier coefficients
ⓘ
almost periodic functions via approximation by trigonometric polynomials with real frequencies ⓘ almost periodic functions via uniform recurrence of values ⓘ |
| defines |
almost periodic function as one whose translates form a relatively compact set in the sup norm
ⓘ
ε-almost period ⓘ |
| field | mathematics ⓘ |
| hasReputation | classic reference on almost periodic functions ⓘ |
| historicalImportance |
foundational work in the modern theory of almost periodicity
ⓘ
systematic exposition of Harald Bohr's theory of almost periodic functions ⓘ |
| includes |
applications to Dirichlet series
ⓘ
applications to ordinary differential equations ⓘ applications to uniform distribution of sequences ⓘ |
| influenced |
Fourier analysis
ⓘ
dynamical systems ⓘ functional analysis ⓘ harmonic analysis on groups ⓘ theory of topological groups ⓘ |
| language | English ⓘ |
| proves |
Bohr's fundamental theorem on almost periodic functions
ⓘ
closure of almost periodic functions under addition and multiplication ⓘ closure of almost periodic functions under translations ⓘ closure of almost periodic functions under uniform limits ⓘ existence of mean values for almost periodic functions ⓘ uniqueness of Bohr–Fourier series for almost periodic functions ⓘ |
| publicationYear | 1947 ⓘ |
| publisher | Chelsea Publishing Company NERFINISHED ⓘ |
| relatedTo |
Besicovitch almost periodic functions
ⓘ
Bochner almost periodic functions ⓘ Stepanov almost periodic functions ⓘ |
| subfield |
analysis
ⓘ
harmonic analysis ⓘ |
| topic | almost periodic functions ⓘ |
| usedIn |
modern harmonic analysis
ⓘ
spectral theory of dynamical systems ⓘ study of quasi-periodic motions ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Almost Periodic Functions Description of subject: Almost Periodic Functions is a foundational mathematical work by Harald Bohr that develops the theory of functions whose values recur with arbitrary precision over time, generalizing the concept of periodicity.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.