(T : UnboundedSelfAdjoint H) (chi : T.domain) (u : ℝ) : T.shift 1 ⟨T.stoneU u (chi : H), T.stoneU_mem_domain u chi⟩ = T.stoneU u (T.shift 1 chi)
ProvedBookProof.ChapterSirkTrotterKato.stoneU_shiftsirkspectral-theorytimepiece
Lean 4 theorem BookProof.ChapterSirkTrotterKato.stoneU_shift (module BookProof.ChapterSirkTrotterKato), source chapter BookProof/ChapterChapterSirkTrotterKato.lean.
Preamble
-- Generated from ChapterSirkTrotterKato.lean — theorem BookProof.ChapterSirkTrotterKato.stoneU_shift
import Mathlib
import Definitions.Def_ChapterSirkTrotterKato
open BookProof.ChapterSirkTrotterKato
noncomputable section
open Filter Topology Asymptotics
open scoped InnerProductSpace
open BookProof.ChapterStoneResolvent
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]Formal statement
theorem BookProof.ChapterSirkTrotterKato.stoneU_shift (T : UnboundedSelfAdjoint H) (chi : T.domain) (u : ℝ) :
T.shift 1 ⟨T.stoneU u (chi : H), T.stoneU_mem_domain u chi⟩
= T.stoneU u (T.shift 1 chi) := by sorrySource