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[]/cmbx10/Definition 1.2. []/cmr10/Siano date due fun-zioni $/cmmi10/f/cmr10/(/
cmmi10/x; y; z/cmr10/)/cmmi10/; g/cmr10/(/cmmi10/x; y; z/cmr10/) : /cmmi10/Y []
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[]/cmr10/Con la II dis-eguaglianza tri-an-go-lare, si ha $[] /cmsy10/^^@ [] ^^T

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 /cmr10/questi lim-iti es-istono perche' $/cmmi10/x/cmr10/(/cmmi10/t/cmr10/)/cm
mi10/; y/cmr10/(/cmmi10/t/cmr10/) /cmsy10/2 /cmmi10/C[]/cmr10/([])$, es-sendo $
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[]/cmr10/Diremo che $/cmmi10/P[] /cmr10/= (/cmmi10/x/cmr10/(/cmmi10/u[]; v[]/cm
r10/)/cmmi10/; y/cmr10/(/cmmi10/u[]; v[]/cmr10/)/cmmi10/; z/cmr10/(/cmmi10/u[];
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0/) /cmsy10/2
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/cmr10/Il vet-tore nor-male di di-rezione di $/cmmi10/^^K$ /cmr10/ha com-po-nen
ti $/cmmi10/A/cmr10/(/cmmi10/u[]; v[]/cmr10/)/cmmi10/; B/cmr10/(/cmmi10/u[]; v[
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[]/cmbx10/Proposition 1.32. []/cmti10/Po-nen-doci sem-pre nelle ipotesi della d
efinizione [[][]1.30[][][],pg.[][]22[][][]],
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/cmbx10/Proof/cmr10/: Poiche' $[] /cmmi10/s/cmr10/(/cmmi10/t/cmr10/) = [] /cmmi
10/t/cmr10/(/cmmi10/s/cmr10/)$, per la propo-sizione [[][]1.4[][][],pg.[][]1[][
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[]/cmr10/Fissiamo una $[] /cmsy10/2 []$/cmr10/, e con-sid-e-ri-amo la fun-zione
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/cmr10/Fissiamo una $[] /cmsy10/2 []$/cmr10/. Come ab-bi-amo visto prima, $/cms
y10/9/cmr10/!/cmmi10/y[] /cmsy10/2 [] /cmr10/:
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[]/cmr10/Poiche' $(/cmmi10/x[]; y[]/cmr10/) /cmsy10/2 []$ /cmr10/e' punto re-go
-lare per $[]$, pos-si-amo sup-porre che $[][] /cmsy10/6/cmr10/=
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 /cmr10/poiche' $[] /cmsy10/2 []$/cmr10/, pos-si-amo scegliere $/cmmi10/^^[$ /c
mr10/in modo da avere $/cmmi10/I/cmr10/([]/cmmi10/; ^^[/cmr10/)[][]$. 
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[]/cmbx10/Definition 2.1. []/cmr10/Un ret-tan-golo chiuso di $[]$, di ver-tici 
prin-ci-pali $/cmmi10/a /cmr10/= (/cmmi10/a[]; a[]; [] ; a[]/cmr10/)/cmmi10/; b
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/cmr10/(**) $[][] [] /cmmi10/T[] /cmr10/= [] /cmmi10/T$ /cmr10/per la pro-pri-e
ta' di finita ad-di-tivita' (vedi [[][]2.5[][][],pg.[][]41[][][]]). 
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[]/cmr10/Per Hp $/cmmi10/f$ /cmr10/e' in-te-gra-bile $/cmsy10/) /cmmi10/f$ /cmr
10/e' lim-i-tata $/cmsy10/)  9[]/cmmi10/M /cmr10/= [] /cmmi10/f/cmr10/(/cmmi10/
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[]/cmr10/Poiche' $/cmmi10/T$ /cmr10/e' chiuso e lim-i-tato, per il cor del thm 
di Weier-strass ([AII,[][]8.35[][][],pg.[][]90[][][]]) 
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[]/cmr10/Trasliamo $/cmmi10/f; g$ /cmr10/in modo da avere $/cmmi10/G[]; G[] /cm
sy10/^^U /cmr10/0$, per poi ap-pli-care il thm [[][]2.16[][][],pg.[][]48[][][]]
: 
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[]/cmbx10/Proposition 2.28. []/cmti10/Sia $/cmmi10/X$ /cmti10/do-minio di $[]$.
 Se $/cmmi10/X$ /cmti10/e' sim-met-rico rispetto all'iperpiano
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[]$/cmmi10/T /cmr10/= [] /cmmi10/;   D /cmr10/= []$ 
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/cmr10/al seg-mento $[] [] []$ di $/cmmi10/D$ /cmr10/cor-risponde il seg-mento 
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/cmr10/Abbiamo visto che $/cmmi10/s[]; s[]; ^^M$ /cmr10/sono curve re-go-lari, 
e poiche' $/cmmi10/F/cmr10/(/cmmi10/T/cmr10/) = /cmmi10/s[][]s[][]^^M$/cmr10/,
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/cmr10/Risolvere l'equazione or-di-naria $(1)$ vuol dire trovare tutti gli el-e
-menti dell'integrale
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[]/cmr10/Mostriamo che ogni soluzione di sec-onda classe e' del tipo $/cmmi10/y
/cmr10/(/cmmi10/x/cmr10/) = /cmmi10/H/cmr10/(/cmmi10/F/cmr10/(/cmmi10/x/cmr10/)
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 $/cmr10/(/cmsy10/^^C/cmr10/)$ ab-bi-amo ap-pli-cato la dis-eguaglianza di Cauc
hy-Schwartz (vedi [AII,[][]8.1[][][],pg.[][]62[][][]]). 
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[]/cmti10/Se $[]/cmmi10/; [] ; []$ /cmti10/sono fun-zioni costanti, al-lora si 
con-sid-era l'equazione
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[]/cmti10/Altrimenti si ap-plica il metodo di vari-azione delle costanti: [[][]
6.26[][][],pg.[][]131[][][]] 
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[]/cmr10/determinante Cauchy-Vandermonde,
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