Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
periodic functions
rapidly decreasing functions |
| gptkbp:expressedIn |
\\sum_{n=-\\infty}^{\\infty} f(n) = \\sum_{k=-\\infty}^{\\infty} \\hat{f}(k)
|
| gptkbp:field |
gptkb:mathematics
Fourier analysis harmonic analysis |
| gptkbp:firstPublished |
1823
|
| https://www.w3.org/2000/01/rdf-schema#label |
Poisson summation formula
|
| gptkbp:namedAfter |
gptkb:Siméon_Denis_Poisson
|
| gptkbp:relatedConcept |
gptkb:Dirac_comb
gptkb:Nyquist–Shannon_sampling_theorem distribution theory modular transformations |
| gptkbp:relatedTo |
gptkb:signal_processing
gptkb:Fourier_transform gptkb:sampling_theory Fourier series |
| gptkbp:sentence |
The sum of a function over all integers equals the sum of its Fourier transform over all integers.
|
| gptkbp:usedIn |
crystallography
engineering modular forms number theory physics image processing spectral analysis lattice point problems signal reconstruction |
| gptkbp:bfsParent |
gptkb:Selberg_trace_formula
|
| gptkbp:bfsLayer |
6
|