OAI/Analysis/LipschitzHilbert/Trees/SourceSpatialSubdivision.lean

GitHub source file

7 declarations, 0 contain sorry, 0 declared as axioms

A bounded rectangle splits into uniformly many half-open cells. Each cell has the exact center bounds used by the ordinary tree estimate.

  1. def OAI.LipschitzHilbert.spatialCellIndex line 12
  2. def OAI.LipschitzHilbert.spatialCellCenter line 13
  3. theorem OAI.LipschitzHilbert.spatialCell_center_bound line 15
  4. theorem OAI.LipschitzHilbert.spatialCell_index_bound line 23
  5. theorem OAI.LipschitzHilbert.spatialCell_count line 36

    Source documentation

    Cells covering an enlarged top are bounded independently of packet count.

    theorem spatialCell_count (K : ℕ) :
    ((Finset.Icc (-(K:ℤ)) K) ×ˢ (Finset.Icc (-(K:ℤ)) K)).card=(2*K+1)^2 := by
…
  6. def OAI.LipschitzHilbert.spatialPacketCell line 45
  7. theorem OAI.LipschitzHilbert.spatialPacketCell_mem line 48