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FourierTf

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FourierTf

гæ (³õÈëÎÄ̳)

ÒýÓûØÌû:
2Â¥: Originally posted by hank612 at 2016-01-06 03:43:40
Â¥Ö÷¿ÉÒÔ¿¼²ì:

f_n(x)=\chi_{}(x), ¼´±ÕÇø¼äµÄʾÐÔº¯Êý.

f_n ÒÀ²â¶ÈÇ÷ÓÚÁã, µ«L_{\infty}·¶ÊýºãµÈÓÚ1.

лл,



ÉÏÊöÁ½¼«ÏÞÏàµÈ£¬ÔòÈõÊÕÁ²µ½f¡£
ÎÒ¼ÆËãÁËһϵĵ½ÁËÉÏÃæµÄ½á¹û£¬ÊÇÄÄÀï³öÎÊÌâÁËÂð£¿
3Â¥2016-01-06 14:30:06
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
²é¿´È«²¿ 6 ¸ö»Ø´ð

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

¡ï ¡ï ¡ï
FourierTf(Edstrayer´ú·¢): ½ð±Ò+3, LatexÓ¦Öú 2016-01-06 04:08:42
Â¥Ö÷¿ÉÒÔ¿¼²ì:

, ¼´±ÕÇø¼äµÄʾÐÔº¯Êý.

ÒÀ²â¶ÈÇ÷ÓÚÁã, µ«·¶ÊýºãµÈÓÚ1.
We_must_know. We_will_know.
2Â¥2016-01-06 03:43:40
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
3Â¥: Originally posted by FourierTf at 2016-01-06 14:30:06
лл,
\forall g\in L_1
\lim_{n\to\infty}\int_R f_ngd\mu=\lim_{n\rightarrow\infty} \int_{} g d\mu=0
\int_R fgd\mu=0
ÉÏÊöÁ½¼«ÏÞÏàµÈ£¬Ôòf_nÈõÊÕÁ²µ½f¡£
ÎÒ¼ÆËãÁËһϵĵ½ÁËÉÏÃæµÄ½á¹û£¬ÊÇÄÄÀï³öÎÊÌâÁËÂð ...

ÎÒÉÏÃæÄǸöÀý×ÓÊÇ´íÎóµÄ, µ±Ê±Ã»ÓÐÀí½âÊÇʲôÒâ˼.

ÎÒ°ÑÀý×ÓÉÓ×öÐÞ¸Ä, Áî, ¾ÍÊǺ¯ÊýÖµÔ½À´Ô½Ð¡, µ«·ÇÁãÇøÓòÔ½À´Ô½´ó,ʹµÃ»ý·ÖÖµºãµÈÓÚ1.

ÄÇô¶ÔÓн纯Êý g(x)=1³£Êýº¯Êý, f_n ÒÀ²â¶ÈÇ÷ÓÚÁã, µ«²»»á ÈõÊÕÁ²ÓÚÁã.  

¿ÉÊÇ, ÎÒÎÞ·¨ÕÒµ½Àý×Ó, ʹµÃ, ¶Ôij¸öL_1º¯Êý h(x), ²»Ç÷ÓÚÁã.
We_must_know. We_will_know.
4Â¥2016-01-07 05:10:40
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

jabile

ľ³æ (ÕýʽдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
ÒýÓûØÌû:
4Â¥: Originally posted by hank612 at 2016-01-07 05:10:40
ÎÒÉÏÃæÄǸöÀý×ÓÊÇ´íÎóµÄ, µ±Ê±Ã»ÓÐÀí½â (w)L_{\infty}ÊÇʲôÒâ˼.

ÎÒ°ÑÀý×ÓÉÓ×öÐÞ¸Ä, Áîf_n(x)=\frac{1}{n}\chi_{(0,n)}(x), ¾ÍÊǺ¯ÊýÖµÔ½À´Ô½Ð¡, µ«·ÇÁãÇøÓòÔ½À´Ô½´ó,ʹµÃ»ý·ÖÖµºãµÈÓÚ1.

ÄÇô¶ÔÓн纯Êý g( ...

nºÍ1/n»»Ò»Ï¾ÍOKÁË

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