Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Periodized Gaussian gridding kernel
Definition
For a real parameter , define the period-one Gaussian gridding kernel by the series
The series is the formal periodization; Local uniform convergence of the periodized Gaussian ↗ proves that it converges absolutely and locally uniformly, so its value is a continuous one-periodic real function. Its Fourier coefficient at is denoted when this integral is used; Fourier series of the periodized Gaussian ↗ computes it exactly. The kernel is nonnegative and satisfies .
Depends on
Used by
- Certified Gaussian gridding for type 1 and type 2 Algorithm
- Exact Gaussian grid alias identity and explicit alias bound Lemma
- Explicit periodized Gaussian spread-tail bound Lemma
- Explicit tail for the periodized Gaussian image sum Lemma
- Fourier series of the periodized Gaussian Lemma
- Local uniform convergence of the periodized Gaussian Lemma
- Certified type-1 Gaussian gridding error and type-2 adjoint bound Theorem
Dependency tree · two levels
9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Jens Keiner, Stefan Kunis, and Antje Vollrath, The Nonequispaced FFT and its Applications, Part I, slides 44–50 and 65–67 (standard reference, not scraped)
- Leslie Greengard and June-Yub Lee, Accelerating the Nonuniform Fast Fourier Transform (standard reference, not scraped)