Theorems · Theorem · number theory
LSeries.abscissaOfAbsConv_convolution_le
∀ (f g : ℕ → ℂ), LSeries.abscissaOfAbsConv (LSeries.convolution f g) ≤ max (LSeries.abscissaOfAbsConv f) (LSeries.abscissaOfAbsConv g)
The abscissa of absolute convergence of f ⍟ g is at most the maximum of those
of f and g.
- Defined in
- Mathlib.NumberTheory.LSeries.Convolution
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
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- Complexstatement and proof · cited by 5,565
- ERealstatement · cited by 793
- LSeries.abscissaOfAbsConvstatement · cited by 50
- LSeries.convolutionstatement · cited by 18
- LSeries.abscissaOfAbsConv_binop_leproof · cited by 3
- LSeriesSummable.convolutionproof · cited by 2
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