The Fourier Integral and Certain of Its Applications
E158220
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Fourier Integral and Certain of Its Applications canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1374535 — 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.
Target entity: The Fourier Integral and Certain of Its Applications Context triple: [Norbert Wiener, notableWork, The Fourier Integral and Certain of Its Applications]
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A.
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.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
D.
Theory and Calculation of Alternating Current Phenomena
Theory and Calculation of Alternating Current Phenomena is a foundational electrical engineering text that systematically develops the mathematical analysis and practical design principles of alternating current (AC) circuits and machinery.
-
E.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: The Fourier Integral and Certain of Its Applications Target entity description: 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.
-
A.
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.
-
B.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
C.
Kailath factorization in linear systems
Kailath factorization in linear systems is a matrix factorization technique used in control and signal processing to efficiently analyze and solve linear dynamical systems.
-
D.
Theory and Calculation of Alternating Current Phenomena
Theory and Calculation of Alternating Current Phenomena is a foundational electrical engineering text that systematically develops the mathematical analysis and practical design principles of alternating current (AC) circuits and machinery.
-
E.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| author | Norbert Wiener ⓘ |
| countryOfPublication |
United States of America
ⓘ
surface form:
United States
|
| field |
Fourier analysis
ⓘ
harmonic analysis ⓘ mathematical analysis ⓘ |
| hasInfluenced |
modern harmonic analysis
ⓘ
probability theory ⓘ signal processing theory ⓘ |
| influencedBy |
David Hilbert
ⓘ
G. H. Hardy ⓘ Henri Lebesgue ⓘ |
| language | English ⓘ |
| notableFor |
applications of Fourier analysis to boundary value problems
ⓘ
rigorous analytic approach to Fourier transforms ⓘ systematic treatment of the Fourier integral ⓘ |
| publicationYear | 1933 ⓘ |
| publisher | Cambridge University Press ⓘ |
| relatedConcept |
Tauberian theorems
ⓘ
surface form:
Wiener Tauberian theorem
Banach algebra ⓘ
surface form:
Wiener algebra
|
| relatedWork | Cybernetics: Or Control and Communication in the Animal and the Machine ⓘ |
| subject |
Bessel functions
ⓘ
Dirichlet problem ⓘ Fourier transform ⓘ
surface form:
Fourier integral
Fourier transform ⓘ Laplace equation ⓘ Poisson integral ⓘ Tauberian theorems ⓘ boundary value problems ⓘ convergence of Fourier series ⓘ generalized harmonic analysis ⓘ harmonic functions ⓘ integral transforms ⓘ orthogonal expansions ⓘ potential theory ⓘ summability methods ⓘ trigonometric series ⓘ |
| targetAudience |
advanced mathematics students
ⓘ
research mathematicians ⓘ |
| timePeriod | 20th century ⓘ |
| usedIn |
communication theory
ⓘ
engineering mathematics ⓘ physics ⓘ |
How these facts were elicited
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Subject: The Fourier Integral and Certain of Its Applications Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.