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Theorems · Theorem · potential theory

InnerProductSpace.HarmonicOnNhd.const_smul

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : FiniteDimensional ℝ E]
  {F : Type u_2} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace ℝ F] {f : E → F} {s : Set E} {c : ℝ},
  InnerProductSpace.HarmonicOnNhd f s → InnerProductSpace.HarmonicOnNhd (c • f) s

Scalar multiples of harmonic functions are harmonic.

Defined in
Mathlib.Analysis.InnerProductSpace.Harmonic.Basic
Cited by
1 results in Mathlib
Foundations
Depth 248 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupNormedSpace
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Around this declaration

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InnerProductSpace.HarmonicContOnCl.const_smul · cited by 1HarmonicContOnCl.const_sm…Set · cited by 53352SetReal · cited by 25697RealNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceInnerProductSpace · cited by 3523InnerProductSpaceFiniteDimensional · cited by 1854FiniteDimensionalInnerProductSpace.HarmonicOnNhd · cited by 24InnerProductSpace.Harmoni…InnerProductSpace.HarmonicAt.const_smul · cited by 2HarmonicAt.const_smulHarmonicOnNhd.const_smulCITED BYCITES

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Cited by1

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