T=T*. σ(T)⊂ℝ. Spectral theorem: T=∫λ dE. Functional calculus.
graph TD
D1["Def: T*=T\nself-adjoint"]
D2["Def: Symmetric\n〈Tx,y〉=〈x,Ty〉 dense"]
D3["Def: Spectral measure\nE(Δ) projection"]
D4["Def: Resolution of identity"]
T1["Thm: σT ⊂ ℝ"]
T2["Thm: Spect thm\nT=∫λ dE_λ"]
T3["Thm: fT = ∫fλ dE\nfunc calculus"]
T4["Thm: Ess spectrum\nσ_ess"]
T5["Thm: Discrete spectrum\nisolated eigenval"]
D1 --> T1
D2 --> D1
D3 --> T2
D4 --> T2
T2 --> T3
T1 --> T4
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 11
Frontier: math.SP