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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�400澶氭墍楂樼瓑闄㈡牎鎷涙敹纰╁＋銆佸崥澹爺绌剁敓鍏ュ鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗�锛岄儴鍒嗗鏍℃洿鏂拌嚦2012骞达紝2013骞�锛涘潎鎻愪緵鏀惰不涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛炴搳鈥�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛炴搳鈥�鑰冨崥瑭﹀嵎搴�鈥� 涓嬭級
2019 骞�瀵ф尝澶у鍗氬＋鐮旂┒鐢熸嫑鐢熻€冭│鍒濊│绉戠洰
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绉戠洰浠ｇ⒓銆佸悕绋�: 2610 娉涘嚱鍒嗘瀽
涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�(g貌u)
锛堜竴锛夎│鍗锋豢鍒嗗€煎強鑰冭│鏅傞枔
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锛堜簩锛夌瓟椤屾柟寮�
绛旈鏂瑰紡鐐洪枆鍗�銆佺瓎瑭︺€傝│鍗风敱瑭﹂鍜岀瓟椤岀礄绲勬垚锛涚瓟妗堝繀闋堝鍦ㄧ瓟椤岀礄锛堢敱鑰冮粸鎻愪緵锛�
鐩告噳(y墨ng)鐨勪綅缃笂銆�
锛堜笁锛夎│鍗烽鍨嬬祼(ji茅)妲�(g貌u)
璀夋槑椤屻€佽▓绠楅
浜�銆佽€冭│绉戠洰绨′粙
娉涘嚱鍒嗘瀽鏄従(xi脿n)浠ｆ暩(sh霉)瀛稿垎鏋愬鐨勯噸瑕佸垎鏀�锛屽叾寤ｅ崥娣卞帤鐨勭悊璜栭珨绯�銆侀珮搴︽鎷殑鐞嗚珫鏂规硶
浠ュ強寤ｆ硾鐨勬噳(y墨ng)鐢ㄥ児鍊煎皪鐝�(xi脿n)浠ｇ瀛告妧琛�(sh霉)鐨勫悇鍊嬮牁(l菒ng)鍩熼兘鐢�(ch菐n)鐢熼噸澶у奖闊�銆傛硾鍑藉垎鏋愮稖鍚堜簡鍑芥暩(sh霉)璜�銆�
骞句綍鍜屼唬鏁�(sh霉)鐨勮榛炶垏鏂规硶锛岀爺绌剁劇绐董绌洪枔涓婄殑鍑芥暩(sh霉)銆佺畻瀛愮悊璜�锛屼互鏇村姞鎶借薄鐨勭磾褰㈠紡鐨勬柟
娉曡В姹轰簡鍒嗘瀽瀛镐腑鐨勮澶氬晱椤�銆傛湰瑾茬▼鏄暩(sh霉)瀛哥郴鐮旂┒鐢熼€插叆鐝�(xi脿n)浠ｆ暩(sh霉)瀛稿缈掑拰鐮旂┒寰堥噸瑕佺殑灏�
妤�(y猫)鍩虹(ch菙)瑾层€傛湰瑾茬▼涓昏浠ョ窔鎬ф硾鍑藉垎鏋愪腑鐨勭┖闁撹珫銆佺畻瀛愬拰娉涘嚱璜栧拰璀滆珫鐐轰富瑕佸収(n猫i)瀹�銆�
涓�銆佽€冭│鍏�(n猫i)瀹瑰強鍏烽珨瑕佹眰
1锛庤窛闆㈢┖闁�
(1) 璺濋洟绌洪枔鐨勬蹇�锛屽収(n猫i)瀹瑰寘鎷畾缇╋紝渚嬪瓙锛堝嚱鏁�(sh霉)绌洪枔鍜屽簭鍒楃┖闁擄級锛岄粸鍒楃殑鏀舵杺鎬�锛屾槧灏�
鐨勯€ｇ簩(x霉)鎬�锛屽収(n猫i)瀹瑰寘鎷枊锛堥枆锛夌悆锛屽収(n猫i)榛�銆侀枊闆�銆侀牁(l菒ng)鍩熺瓑姒傚康锛岃窛闆㈢殑绛夊児鎬�锛屾槧灏勭殑閫ｇ簩(x霉)鎬�
绛�锛�
(2) 璺濋洟绌洪枔鐨勯枆闆嗭紝鍏�(n猫i)瀹瑰寘鎷窛闆㈢┖闁撶殑闁夐泦锛岄泦鍚堢殑闁夊寘锛岄泦鍚堢殑绋犲瘑鎬у拰璺濋洟绌洪枔鐨�
鍙垎鎬�锛屽垪绶婇泦鍜岃窛闆㈢┖闁撶殑鍒楃穵鎬�锛�
(3) 璺濋洟绌洪枔鐨勫畬鍌欐€э紝鍏�(n猫i)瀹瑰寘鎷� Cauchy 鍒�锛屽畬鍌欒窛闆㈢┖闁撶殑瀹氱京锛屽畬鍌欑┖闁撹垏涓嶅畬鍌欑┖
闁撹垑渚嬶紝璺濋洟绌洪枔鐨勫畬鍌欏寲锛�
(4) 瀹屽倷璺濋洟绌洪枔鐨勬€ц唱(zh矛)锛屽収(n猫i)瀹瑰寘鎷枆闆嗗瀹氱悊锛孊anach 澹撶府鏄犵収鍘熺悊鍙婂叾鎳�(y墨ng)鐢ㄣ€�
2锛庤肠鑼冪┖闁�
(1) 璩﹁寖绌洪枔鐨勬蹇�锛屽収(n猫i)瀹瑰寘鎷肠鑼冪┖闁撳拰 Banach 绌洪枔瀹氱京锛屼緥瀛愶紙鍑芥暩(sh霉)绌洪枔鍜屽簭鍒楃┖闁擄級锛�
鑼冩暩(sh霉)閫ｇ簩(x霉)鎬�锛岃寖鏁�(sh霉)鑸囪窛闆㈢殑闂�(gu膩n)绯�锛岄粸鍒楃殑鏀舵杺鎬�锛�
(2) 瀹屽倷璩﹁寖绌洪枔锛屽収(n猫i)瀹瑰寘鎷肠浜堜笉鍚岃寖鏁�(sh霉)鐨勯€ｇ簩(x霉)鍑芥暩(sh霉)绌洪枔锛岃肠鑼冪┖闁撶殑瀹屽倷鍖�锛岄噸瑕佺殑瀹�
鍌欑┖闁撻尟瑾わ紒鏈壘鍒板紩鐢ㄦ簮銆傜┖闁撳拰閷锛佹湭鎵惧埌寮曠敤婧�銆傜┖闁�锛�
(3) 璩﹁寖绌洪枔鐨勭殑骞句綍绲�(ji茅)妲�(g貌u)锛屽収(n猫i)瀹瑰寘鎷嚫闆�锛屽瓙绌洪枔鍜� Riesz 寮曠悊锛�
(4) 鏈夐檺缍肠鑼冪┖闁�锛屽収(n猫i)瀹瑰寘鎷寖鏁�(sh霉)绛夊児鎬�锛屾湁闄愮董璩﹁寖绌洪枔鐨勫咕浣曠壒寰�銆�
3锛庡収(n猫i)绌嶇┖闁撳拰 Hilbert 绌洪枔
(1) 鍏�(n猫i)绌嶇┖闁撶殑鍩烘湰鎬ц唱(zh矛)锛屽寘鎷収(n猫i)绌�銆佸収(n猫i)绌嶇┖闁�锛屽収(n猫i)绌嶅拰鑼冩暩(sh霉)鐨勯棞(gu膩n)绯�銆佸収(n猫i)绌嶇┖闁撶壒寰�銆丠ilbert
绌洪枔鐨勫畾缇╋紝涓€浜涘吀鍨嬬殑鍏�(n猫i)绌嶇┖闁�銆丠ilbert 绌洪枔渚嬪瓙锛�
(2) 姝ｄ氦鍜屾浜ゅ垎瑙�锛屽寘鎷浜ゅ拰姝ｄ氦瑁滅殑瀹氱京锛屽嚫闆嗙殑鏈€浣抽€艰繎锛孒ilbert 绌洪枔姝ｄ氦鍒嗚В
瀹氱悊锛�
(3) 姝ｄ氦绯诲拰姝ｄ氦鎶曞奖锛屽寘鎷収(n猫i)绌嶇┖闁撴浜ょ郴鍜屾浜ゆ姇褰卞畾缇�锛孎(xi脿n)ourier 绱氭暩(sh霉)锛孊essel 涓嶇瓑
寮忚垏 Fourier 绱氭暩(sh霉)鐨勬敹鏂傛€�锛�
(4) 姝ｄ氦鍩哄拰姝ｄ氦鍒楃殑瀹屽倷鎬э紝鍖呮嫭姝ｄ氦鍩哄拰姝ｄ氦鍒楃殑瀹屽倷鎬у畾缇�锛屾浜ゅ垪鐨勫畬鍌欐€х殑鍥涘€�
鍍规€ф弿杩�锛�
(5) 鍙垎 Hilbert 绌洪枔鐨勭瓑璺濆悓妲�(g貌u)锛屽寘鎷窔鎬х劇闂�(gu膩n)绲勬浜ゅ寲绠楁硶锛屽彲鍒� Hilbert 绌洪枔鑸囬尟瑾�锛�
鏈壘鍒板紩鐢ㄦ簮銆�
4锛庢湁鐣岀窔鎬х畻瀛愬拰绶氭€ф硾鍑�
(1) 鏈夌晫绶氭€х畻瀛愬拰鏈夌晫绶氭€ф硾鍑斤紝鍖呮嫭瀹冨€戠殑瀹氱京锛屼竴浜涙湁鐣岀窔鎬х畻瀛愬拰鏈夌晫绶氭€ф硾鍑界殑
渚嬪瓙锛岀窔鎬х畻瀛愭湁鐣屾€у拰閫ｇ簩(x霉)鎬х殑闂�(gu膩n)绯伙紝绶氭€х畻瀛愯肠鑼冪┖闁撳畾缇╋紙閬庣▼锛�锛屼竴浜涘叿楂旀湁鐣岀窔
鎬х畻瀛愭垨娉涘嚱鑼冩暩(sh霉)鐨勮▓绠�銆�
(2) 鏈夌晫绶氭€х畻瀛愮┖闁撶殑鏀舵杺鍜屽畬鍌欐€�锛屽収(n猫i)瀹瑰寘鎷湁鐣岀窔鎬х畻瀛愬垪鐨勮寖鏁�(sh霉)鏀舵杺瀹氱京鍙婂叾绛夊児
鎬э紝鏈夌晫绶氭€х畻瀛愬垪鐨勫挤鏀舵杺鐨勫畾缇╀互鍙婅垏鑼冩暩(sh霉)鏀舵杺鐨勯棞(gu膩n)绯�锛岀畻瀛愮┖闁擄紙娉涘嚱绌洪枔锛夌殑瀹屽倷
鎬�銆�
(3) 涓€鑷存湁鐣屽師鐞�锛屽寘鎷� Baire 缍卞畾鐞�锛屽強鍏跺悇绋〃鐝�(xi脿n)褰㈠紡锛孊anach-Steinhaus 涓€鑷存湁鐣�
鍘熺悊鍙婂叾閫嗗惁鍛介锛屾湁鐣岀窔鎬х畻瀛愮┖闁撳挤鏀舵杺鎰忕京涓嬬殑瀹屽倷鎬с€�
(4) 闁嬫槧灏勫畾鐞嗚垏閫嗙畻瀛愬畾鐞�锛屽寘鎷€嗙畻瀛愬畾缇�锛屾湁鐣岄€嗙畻瀛愬瓨鍦ㄧ殑鍏呭垎姊濅欢锛岄枊鏄犲皠瀹氱悊
鍙婂叾璀夋槑锛岄€嗙畻瀛愬畾鐞嗭紝Banach 绌洪枔鐨勮寖鏁�(sh霉)绛夊児瀹氱悊銆�
(5) 闁夌畻瀛愬拰闁夊湒鍍忓畾鐞�锛屽寘鎷枆绠楀瓙鐨勫畾缇�锛岃垏闁夊湒鍍忕殑绛夊児鎬э紝绶氭€х畻瀛愮殑闁夋€�锛岃垏鏈�
鐣屾€у拰闁夊畾缇╁煙鐨勯棞(gu膩n)绯伙紝涓€浜涢噸瑕侀枆绠楀瓙鐨勪緥瀛�锛岄枆鍦栧儚瀹氱悊銆�
5锛庡叡杌涚┖闁撳拰鍏辫粵绠楀瓙
(1) Hahn-Banach 寤舵嫇瀹氱悊锛堝京(f霉)褰㈠紡鍜屽褰㈠紡锛夊強鍏跺咕鍊嬮噸瑕佹帹璜�锛屽畠鍊戝湪鍑搁泦鍒嗛洟涓殑鎳�(y墨ng)
鐢�锛�
(2) 鍏辫粵绌洪枔锛屽寘鎷叡杌涚┖闁撶殑瀹氱京锛屽咕鍊嬮噸瑕佺┖闁撶殑鍏辫粵绌洪枔锛�
(3) Hilbert 绌洪枔鐨勫叡杌涚┖闁�锛屽寘鎷� Riesz 琛ㄧず瀹氱悊锛孒ilbert 绌洪枔鐨勫叡杌涚┖闁撳湪鍏辫粵鍚屾(g貌u)
鎰忕京涓嬪拰鑷韩绛夊悓锛孒ilbert 绌洪枔鐨勫叡杌涚畻瀛�锛屽寘鎷畠鐨勫畾缇╁拰鎬ц唱(zh矛)锛屾湁鐣岀窔鎬х畻瀛愮殑鍊煎煙
鑸囧畠鐨勫叡杌涚畻瀛愰浂绌洪枔鐨勯棞(gu膩n)绯�锛�
(4) Hilbert 绌洪枔涓殑鑷叡杌涚殑鏈夌晫绶氭€х畻瀛�锛屽寘鎷畠鐨勫畾缇╁拰鎬ц唱(zh矛)锛屽咕鍊嬮噸瑕佺殑鑷叡杌涚殑
鏈夌晫绶氭€х畻瀛�锛屾湁鐣岀窔鎬х畻瀛愮殑 Cartesian 鍒嗚В锛�
(5) Banach 绌洪枔鐨勫叡杌涚畻瀛�锛屽寘鎷畠鐨勫畾缇╁拰鎬ц唱(zh矛)锛孒ilbert 绌洪枔鑸� Banach 绌洪枔鐨勫畾缇╄粵
绠楀瓙鐨勯棞(gu膩n)绯�锛岀┖闁撹嚜鍙嶆€х殑瀹氱京锛屽咕椤為噸瑕佺殑鑷弽绌洪枔锛屽急鏀舵杺鍙婂叾鐩搁棞(gu膩n)鎬ц唱(zh矛)锛屽挤鏀舵杺鑸囧急
鏀舵杺鐨勯棞(gu膩n)绯�锛�
(6) 绶氭€х畻瀛愮殑璀滅悊璜�锛屽寘鎷畾缇╄垏渚嬪瓙锛岄爯(y霉)瑙ｅ紡銆佽瓬鍗婂緫鍙婅▓绠楀畾鐞�銆�
鍥涖€佸弮鑰冩暀鏉愭垨涓昏鍙冭€冩浉
1. 鏁欐潗
[1] 娉涘嚱鍒嗘瀽璎涚京锛堜笂鍐婏級锛屽嫉鎭叾锛屾灄婧愭笭钁�锛屽寳浜ぇ瀛稿嚭鐗堢ぞ锛屽寳浜�锛�2015.
2. 鍙冭€冩浉鐩�
[1] 瀵﹁畩鍑芥暩(sh霉)鑸囨硾鍑藉垎鏋愭瑕侊紙绗簩鍐婏級锛岄劖缍銆佺帇鑱叉湜绶ㄨ憲锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2010.
[2] 瀵﹁畩鍑芥暩(sh霉)鑸囨硾鍑藉垎鏋愶紙涓嬪唺锛�锛屽閬撹绶ㄨ憲锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2010.
[3] 瀵﹁畩鍑芥暩(sh霉)鑸囨硾鍑藉垎鏋愬熀绀�(ch菙)锛岀▼鍏惰锛屽嫉濂犲畽绶ㄨ憲锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2004.
[4] Functional Analysis锛學alter Rudin锛孧c Graw Hill Education锛�1999.
鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘紝璜嬭伅(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€嬩汉瑙€榛烇紝鑸囨湰缍�(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂�(gu膩n)鍏�(n猫i)瀹�銆�
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鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
