【SEOテキスト】宇田雄一「古典物理学」2-3-A数学用語の定義,F1の定義:F1={f|f∈F1 and∀t∈R({4});|∂4f(t,□)|<1},F2,nの定義:∀n∈N;F2,n={f|f∈F2,n
and∀k∈{1,・・・,n};f(□,□,k)∈F1},F4,nの定義:∀n∈N;F4,n={f|f∈F4,n and f(N2,n)∈F2,n},F12の定義:F12={f|∃m∈N;f∈F12,m
and f(N2,m)∈F2,m}∪{0∈R},F14の定義:F14={f|∃m∈N;f∈F14,m and f(N2,m)∈F2,m}∪F3,uniの定義:∀a∈R(2);uni(a)∈N01(N01)and∀ξ∈N01;【1】and【2】【1】[[uni(a)](ξ)](4)=a(2)ξ(4)【2】∀i∈3;[[uni(a)](ξ)](i)=a(1)ξ(i),couの定義:∀α∈R(2);cou(α)∈F3(F3)and∀f∈F3;【1】and【2】【1】[[cou(α)](f)](□,1)=α(1)f(□,1)【2】[[cou(α)](f)](□,2)=α(2)f(□,2),traの定義:∀x∈N01;tra(x)∈N01(N01)and∀ξ∈N01;[tra(x)](ξ)=ξ+x,rotの定義:∀r∈SO(3);rot(r)∈N01(N01)and∀ξ∈N01;【1】and【2】【1】[[rot(r)](ξ)](4)=ξ(4)【2】∀i∈3;[[rot(r)](ξ)](i)=3∑j=1
r(i,j)ξ(j),corの定義:∀r∈SO(3);cor(r)∈F3(F3)and∀f∈F3;∀(i,k)∈N3;[[cor(r)](f)](i,k)=3∑j=1
r(i,j)f(j,k),galの定義:∀v∈R(3);gal(v)∈N01(N01)and∀ξ∈N01;【1】and【2】【1】[[gal(v)](ξ)](4)=ξ(4)【2】∀i∈3;[[gal(v)](ξ)](i)=ξ(i)-v(i)ξ(4)
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