Theorems · Theorem · functional analysis
SchwartzMap.norm_le_seminorm
∀ (𝕜 : Type u_2) {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedField 𝕜] [inst_5 : NormedSpace 𝕜 F]
[inst_6 : SMulCommClass ℝ 𝕜 F] (f : SchwartzMap E F) (x₀ : E), ‖f x₀‖ ≤ (SchwartzMap.seminorm 𝕜 0 0) f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- SMulCommClassstatement and proof · cited by 1,927
- pow_zeroproof · cited by 1,094
- NormedFieldstatement and proof · cited by 1,084
- Seminormstatement · cited by 272
- SchwartzMapstatement and proof · cited by 251
- SchwartzMap.seminormstatement and proof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- SchwartzMap.norm_toLp_top_leproof · cited by 1
- SchwartzMap.convolution_applyproof · cited by 0