Theorems · Theorem · harmonic analysis
SchwartzMap.tsum_eq_tsum_fourier
∀ (f : SchwartzMap ℝ ℂ) (x : ℝ), ∑' (n : ℤ), f (x + ↑n) = ∑' (n : ℤ), (FourierTransform.fourier f) ↑n * (fourier n) ↑x
Poisson's summation formula for Schwartz functions.
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- Foundations
- Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound
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- Complexstatement and proof · cited by 5,565
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- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement · cited by 348
- SchwartzMapstatement and proof · cited by 251
- AddCirclestatement · cited by 189
- FourierTransform.fourierstatement and proof · cited by 130
- one_lt_twoproof · cited by 67
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