Theorems · Definition · functional analysis

SchwartzMap.toBoundedContinuousFunction

{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] → SchwartzMap E F → BoundedContinuousFunction E F

Schwartz functions as bounded continuous functions

Defined in: Mathlib.Analysis.Distribution.SchwartzSpace.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · 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
BoundedContinuousFunctionstatement · cited by 511
SchwartzMapstatement and proof · cited by 251
SchwartzMap.seminormproof · cited by 16
SchwartzMap.continuousproof · cited by 7
BoundedContinuousFunction.ofNormedAddCommGroupproof · cited by 6

Cited by7

Results whose statement or proof uses this declaration.

SchwartzMap.toBoundedContinuousFunctionCLMproof · cited by 2
SchwartzMap.toZeroAtInfty_toBCFstatement · cited by 1
SchwartzMap.norm_toBoundedContinuousFunction_lestatement · cited by 0
SchwartzMap.toBoundedContinuousFunction_applystatement · cited by 0
SchwartzMap.toContinuousMapproof · cited by 0
SchwartzMap.norm_toZeroAtInftystatement and proof · cited by 0
SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_onestatement · cited by 0