²é¿´: 1632  |  »Ø¸´: 8
µ±Ç°Ö»ÏÔʾÂú×ãÖ¸¶¨Ìõ¼þµÄ»ØÌû£¬µã»÷ÕâÀï²é¿´±¾»°ÌâµÄËùÓлØÌû

zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

[ÇóÖú] Çë½ÌHilbert ±ä»»¼òµ¥ÎÊÌâÒ»¸ö ÒÑÓÐ2È˲ÎÓë

Çë¸÷λ°ïÖúÇóÒ»¸öº¯ÊýµÄHilbert ±ä»»£¬ ¶àл
f(x) = |x|^r.  (x is real, 0<r<1).
ÎÒÖªµÀ´ð°¸£¬¾ÍÊÇŪ²»³öÁË£¬Ò²¾ÍÊÇÍüÁËCauchy principal value integral.  
Hilbert ±ä»¯¼ûͼƬ
¶àл°ïæ¡£ Äı¾²Î¿¼Êé½²µÄ±È½Ï¶à¡£

Çë½ÌHilbert ±ä»»¼òµ¥ÎÊÌâÒ»¸ö
bd0946c981b4f7cb2ae134166cab53fc.png
»Ø¸´´ËÂ¥

» ²ÂÄãϲ»¶

» ±¾Ö÷ÌâÏà¹Ø¼ÛÖµÌùÍÆ¼ö£¬¶ÔÄúͬÑùÓаïÖú:

Сľ³æ¸øÎÒÎÂů£¬¸øÎÒÏ£Íû£¬°®¾ÍÒª°®Ð¡Ä¾³æ¡£
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by feixiaolin at 2014-08-08 12:57:54
|x|^r=x^r*sgn(x)
H=x^r*sgn(x)¾í»ý1/(pi*t)
ÔÚÆµÓò´¦Àí£¬±ä»ØÀ´¡£

Can you expand
ÔÚÆµÓò´¦Àí£¬±ä»ØÀ´
a little bit more?

Thanks a lot. We are on the right track.
Сľ³æ¸øÎÒÎÂů£¬¸øÎÒÏ£Íû£¬°®¾ÍÒª°®Ð¡Ä¾³æ¡£
3Â¥2014-08-09 00:59:38
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
²é¿´È«²¿ 9 ¸ö»Ø´ð

feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

|x|^r=x^r*sgn(x)
H[|x|^r]=x^r*sgn(x)¾í»ý1/(pi*t)
ÔÚÆµÓò´¦Àí£¬±ä»ØÀ´¡£
2Â¥2014-08-08 12:57:54
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

Edstrayer

°æÖ÷ (ÖøÃûдÊÖ)

·½´ç¶·ÊÒСÌìµØÕýÆøÃÔÂþ´óÊÀ½ç

http://wenku.baidu.com/link?url= ... iBflJKO4E3li-JtFJzC
ÕâÆªÂÛÎÄ̸µ½ÁËHilbert±ä»»¼°Æä»ù±¾ÐÔÖÊ£¬¿ÉÒԲο¼Âð£¿

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

Çà´ÐËêÔÂÊ¥µ®Ò¹£¬ÀËÂþ¸èÎèÓ­ÐÂÄê¡£
4Â¥2014-08-09 08:19:57
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ztt405

гæ (СÓÐÃûÆø)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
ÖÜÃñÇ¿µÄ"µ÷ºÍ·ÖÎö½²Òå"µÚ112Ò³Óн²L^2ÉϵÄHilbert±ä»», Äã¿ÉÒԲο¼.
5Â¥2014-08-09 08:53:21
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[¿¼ÑÐ] 070300»¯Ñ§319Çóµ÷¼Á +7 ½õÀð0909 2026-03-17 7/350 2026-03-21 03:46 by JourneyLucky
[¿¼ÑÐ] 265Çóµ÷¼Á +3 Jack?k?y 2026-03-17 3/150 2026-03-21 03:17 by JourneyLucky
[¿¼ÑÐ] »ª¶«Ê¦·¶´óѧ-071000ÉúÎïѧ-293·Ö-Çóµ÷¼Á +3 Ñо¿ÉúºÎÑþÃ÷ 2026-03-18 3/150 2026-03-21 01:30 by JourneyLucky
[¿¼ÑÐ] 280Çóµ÷¼Á +7 ¹¾ààÏþÏþ 2026-03-18 8/400 2026-03-21 01:27 by JourneyLucky
[¿¼ÑÐ] Ò»Ö¾Ô¸Î÷ÄϽ»´ó£¬Çóµ÷¼Á +5 ²Ä»¯ÖðÃÎÈË 2026-03-18 5/250 2026-03-21 00:26 by JourneyLucky
[¿¼ÑÐ] 274Çóµ÷¼Á +10 S.H1 2026-03-18 10/500 2026-03-20 23:51 by JourneyLucky
[¿¼ÑÐ] 295Çóµ÷¼Á +4 Ò»Ö¾Ô¸¾©Çø211 2026-03-18 6/300 2026-03-20 23:41 by JourneyLucky
[¿¼ÑÐ] 308Çóµ÷¼Á +3 °¢½ã°¢½ã¼Ò°¡ 2026-03-18 3/150 2026-03-20 23:24 by JourneyLucky
[¿¼ÑÐ] ÖÐÄÏ´óѧ»¯Ñ§Ñ§Ë¶337Çóµ÷¼Á +3 niko- 2026-03-19 6/300 2026-03-20 21:58 by luoyongfeng
[¿¼ÑÐ] Ò»Ö¾Ô¸¼ªÁÖ´óѧ²ÄÁÏѧ˶321Çóµ÷¼Á +11 Ymlll 2026-03-18 15/750 2026-03-20 19:40 by ¶¡¶¡*
[»ù½ðÉêÇë] ѧУÒѾ­Ìá½»µ½NSFC£¬»¹ÄÜÐÞ¸ÄÂ𣿠40+4 babangida 2026-03-19 8/400 2026-03-20 15:58 by babero
[¿¼ÑÐ] 08¹¤Ñ§µ÷¼Á +5 Óû§573181 2026-03-20 5/250 2026-03-20 15:47 by xia_2003
[¿¼ÑÐ] 286·ÖÈ˹¤ÖÇÄÜרҵÇëÇóµ÷¼ÁÔ¸Òâ¿ç¿¼£¡ +3 lemonzzn 2026-03-17 4/200 2026-03-20 11:04 by lemonzzn
[¿¼ÑÐ] ²ÄÁÏѧ˶318Çóµ÷¼Á +5 February_Feb 2026-03-19 5/250 2026-03-19 23:51 by 23Postgrad
[¿¼ÑÐ] 320Çóµ÷¼Á0856 +3 ²»ÏëÆðÃû×Ö112 2026-03-19 3/150 2026-03-19 22:53 by ѧԱ8dgXkO
[¿¼ÑÐ] 346Çóµ÷¼Á[0856] +3 WayneLim327 2026-03-16 6/300 2026-03-19 11:21 by WayneLim327
[¿¼ÑÐ] 085601ר˶£¬×Ü·Ö342Çóµ÷¼Á£¬µØÇø²»ÏÞ +5 share_joy 2026-03-16 5/250 2026-03-18 14:48 by haxia
[¿¼ÑÐ] 334Çóµ÷¼Á +3 Ö¾´æ¸ßÔ¶ÒâÔÚ»úÐ 2026-03-16 3/150 2026-03-18 08:34 by lm4875102
[¿¼ÑÐ] 0703»¯Ñ§µ÷¼Á 290·ÖÓпÆÑо­Àú£¬ÂÛÎÄÔÚͶ +7 ÄåÄågk 2026-03-14 7/350 2026-03-16 10:12 by houyaoxu
[¿¼ÑÐ] 327Çóµ÷¼Á +6 ʰ¹âÈÎȾ 2026-03-15 11/550 2026-03-15 22:47 by ʰ¹âÈÎȾ
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û