泛函分析11new

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1、1›˜ù1341341›˜ù½½½nnn4.2.X•E‚5˜m§MX•Ef˜m§p(x)•Xþg!ýéà5•¼§f•MþE‚5•¼…jf(x)jp(x);8x2M"K•3XþE‚5•¼g¦g=f±9jg(x)jp(x);8x2X"M1341›˜ù½½½nnn4.2.X•E‚5˜m§MX•Ef˜m§p(x)•Xþg!ýéà5•¼§f•MþE‚5•¼…jf(x)jp(x);8x2M"K•3XþE‚5•¼g¦g=f±9jg(x)jp(x);8x2X"M5µp(x)g!ýéà5=

2、)p(x)0"1341›˜ù½½½nnn4.2.X•E‚5˜m§MX•Ef˜m§p(x)•Xþg!ýéà5•¼§f•MþE‚5•¼…jf(x)jp(x);8x2M"K•3XþE‚5•¼g¦g=f±9jg(x)jp(x);8x2X"M5µp(x)g!ýéà5=)p(x)0"*2p(x)=p(x)+p(x)p()=01341›˜ù½½½nnn4.2.X•E‚5˜m§MX•Ef˜m§p(x)•Xþg!ýéà5•¼§f•MþE‚5•¼…jf(x)jp(x);8x2M"K•3

3、XþE‚5•¼g¦g=f±9jg(x)jp(x);8x2X"M5µp(x)g!ýéà5=)p(x)0"*2p(x)=p(x)+p(x)p()=0yyy²²²X•´¢‚5˜m§M´¢f˜m§p(x)´Xþg!à5•¼§1341›˜ù½½½nnn4.2.X•E‚5˜m§MX•Ef˜m§p(x)•Xþg!ýéà5•¼§f•MþE‚5•¼…jf(x)jp(x);8x2M"K•3XþE‚5•¼g¦g=f±9jg(x)jp(x);8x2X"M5µp(x)g!ýéà5=)p(x)

4、0"*2p(x)=p(x)+p(x)p()=0yyy²²²X•´¢‚5˜m§M´¢f˜m§p(x)´Xþg!à5•¼§f0(x)=Ref(x)´Mþ˜‡¢‚5•¼…f0(x)=Ref(x)jf(x)jp(x);8x2M"134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"½Âg(x)=g0(x)ig0(ix);8x2X,Kg

5、(x)•Œ!¢à5•¼§134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"½Âg(x)=g0(x)ig0(ix);8x2X,Kg(x)•Œ!¢à5•¼§g(ix)=g0(ix)ig0(x)=g0(ix)+ig0(x)=ig(x)134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"½Âg(x)=g0(x)ig0(ix);8x2X,Kg(x)•Œ!¢à5•¼§g(ix)=g0(ix)

6、ig0(x)=g0(ix)+ig0(x)=ig(x)=)8;2R,kg((+i)x))=g(x)+g(ix)=g(x)+ig(x)=(+i)g(x),134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"½Âg(x)=g0(x)ig0(ix);8x2X,Kg(x)•Œ!¢à5•¼§g(ix)=g0(ix)ig0(x)=g0(ix)+ig0(x)=ig(x)=)8;2R,kg((+i)x))=g(x)+g(ix)=

7、g(x)+ig(x)=(+i)g(x),)g(x)Eà5§g(x)•XþE‚5•¼"134dHahn-Banach½n§•3Xþ¢‚5•¼g0¦g0=Mf09g0(x)p(x);8x2X"½Âg(x)=g0(x)ig0(ix);8x2X,Kg(x)•Œ!¢à5•¼§g(ix)=g0(ix)ig0(x)=g0(ix)+ig0(x)=ig(x)=)8;2R,kg((+i)x))=g(x)+g(ix)=g(x)+ig(x)=(+i)g(x),)g(x)Eà5§g(x)•Xþ

8、E‚5•¼"x2Mž§g(x)=g0(x)ig0(ix)=f0(x)if0(ix)=Ref(x)iRef(ix)=f(x)"135135jg(x)j=eitg(x)=g(eitx)135jg(x)j=eitg(x)=g(eitx)=Reg(eitx)=g0(eitx)135jg(x)j=eitg(x)=g(eitx)=Reg(eitx)=g0(eitx)p(eitx)=jeitjp(x)=p(x)8x2X135jg