Distribution Support

DEFINITION

$s p t_{T} := R ∖ ⋃ {⟨ T | φ ⟩ = 0 \forall φ \in D; s p t_{φ} \subseteq Ω open}$

Smallest Closed Set $C \in \overset{―}{Ω}$ WHERE $⟨ T | ϕ ⟩ \neq 0$ $\forall ϕ \in$ $D (Ω ∖ C)$ .

Example 1

$s p t$ of $T_{x^{2} - x}$ ?

$⟨ T_{x^{2} - x} | φ ⟩$ = $\int (x^{2} - x) \cdot φ (x) \cdot d x$
It's = $0$ WHEN $x^{2} - x = 0$ → ${\begin{cases} x = 0 \\ x = 1 \end{cases}$ BUT $s p t \neq R ∖ {0, 1}$ CAUSE spt definition imply Closed Set ⇒ I must also include the extremes → $s p t = R$

QUESTIONS

<% tp.file.cursor(20) %>

<% tp.file.cursor(21) %>

DEFINITION

#h-t LINKED