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Clear filtersnorm_fourier_le_integral_deriv_div
Plain-language statement
Fourier-transform decay from an integrable derivative: for integrable, differentiable g with integrable derivative, ‖𝓕 g w‖ ≤ (∫ ‖deriv g x‖) / (2π·|w|).
Source project: Prime Number Theorem and More
Person-level attribution pending.
norm_oscillatory_integral_le_integral_deriv_div
Plain-language statement
The oscillatory-integral form of the decay bound: for 0 < T, ‖∫ g y · exp(T·i·y)‖ ≤ (∫ ‖deriv g x‖) / T.
Source project: Prime Number Theorem and More
Person-level attribution pending.
norm_oscillatory_integral_le_integral_deriv_div_abs
Plain-language statement
The |T| variant of the oscillatory-integral decay bound: for T ≠ 0, ‖∫ g y · exp(T·i·y)‖ ≤ (∫ ‖deriv g x‖) / |T|.
Source project: Prime Number Theorem and More
Person-level attribution pending.