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(xu茅)鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗堬紝閮ㄥ垎瀛�(xu茅)鏍℃洿鏂拌嚦2012骞�锛�2013骞�锛涘潎鎻愪緵鏀惰不(f猫i)涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛�(di菐n)鎿娾€�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛�(di菐n)鎿娾€�鑰冨崥瑭﹀嵎搴�鈥� 涓嬭級 

纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│澶х侗鑰冭│绉戠洰鍚嶇ū: 娉涘嚱鍒嗘瀽涓€銆佹彺寮曟暀鏉�          

銆婃硾鍑藉垎鏋愩€嬬浜岀増 楂樼瓑鏁欒偛鍑虹増绀� 姹熸兢鍫� 瀛杽鍒╃法

浜�銆佽€冭│瑕佹眰

瑕佹眰鑰冪敓鍏ㄩ潰绯荤当(t菕ng)鍦版帉鎻℃硾鍑藉垎鏋愮殑鍩烘湰姒傚康鍙婂熀鏈畾鐞嗭紝骞朵笖鑳介潏娲婚亱(y霉n)鐢�锛屽叿鍌欒純寮�(qi谩ng)鐨勫垎鏋愬晱椤岃垏瑙ｆ焙鍟忛鐨勮兘鍔�銆�

涓夈€佽€冭│鍏�(n猫i)瀹�

锛堜竴锛夎窛闆㈢窔鎬х┖闁�

1锛� 璺濋洟绶氭€х┖闁撶殑瀹氱京锛屽父瑕嬬殑璺濋洟绶氭€х┖闁撶殑璺濋洟瀹氱京鍙婂叾鎬ц唱(zh矛)銆�

2锛� 璺濋洟绌洪枔涓殑鎷�?f霉)娴滎労x锛屽彲鍒嗙┖闁�銆�

3锛� Cauchy搴忓垪鐨勬€ц唱(zh矛)锛岃窛闆㈢┖闁撶殑瀹屽倷鎬с€�

4锛� 鍒楃穵闆�锛屽畬鍏ㄦ湁鐣岄泦鐨勫畾缇╁強瀹冨€戜箣闁撶殑闂�(gu膩n)绯�銆�

5锛� 璩﹁寖绶氭€х┖闁撳畾缇╋紱鑼冩暩(sh霉)鑸囪窛闆㈢殑闂�(gu膩n)绯�锛涙湁闄愮董璩﹁寖绶氭€х┖闁撶殑绲�(ji茅)妲�(g貌u)銆�

6锛� 璩﹁寖绶氭€х┖闁撲笂鐨勭窔鎬х畻瀛愬強鏈夌晫绶氭€х畻瀛愮殑瀹氱京銆佹€ц唱(zh矛)鑸囪▓绠楁柟娉�銆�

7锛� 甯歌绌洪枔浠ュ強绛夌┖闁撲腑璺濋洟鑸囪寖鏁�(sh霉)涔嬮枔鐨勫畾缇╁強闂�(gu膩n)绯汇€傛帉鎻￠€欎簺绌洪枔鐨勫彲鍒嗘€�锛屽畬鍌欐€у強鎷�?f霉)婀啀|(zh矛)銆�

8锛� 澹撶府鏄犲皠瀹氱京锛屾帉鎻″绺槧璞″師鐞�锛屽苟鑳界啛绶寸殑鎳�(y墨ng)鐢ㄥ畾鐞嗚В姹哄晱椤屻€備簡瑙ｅ绺槧璞″師鐞嗗湪鐞嗚珫涓婄殑鍏稿瀷鎳�(y墨ng)鐢�銆�

锛堜簩锛塇ilbert绌洪枔

1锛� 鍏�(n猫i)绌嶇┖闁撶殑瀹氱京锛屾€ц唱(zh矛)锛涘収(n猫i)绌嶈垏鑼冩暩(sh霉)銆佽窛闆箣闁撶殑闂�(gu膩n)绯�銆�

2锛� 璩﹁寖绶氭€х┖闁撴垚鐐哄収(n猫i)绌嶇┖闁撶殑姊濅欢锛屽父瑕嬭肠鑼冪窔鎬х┖闁撴槸鍚︽垚鐐哄収(n猫i)绌嶇┖闁撶殑鍒ゅ垾銆�

3锛� 鎺屾彙鍏�(n猫i)绌嶇┖闁�鐨勫畾缇╁強鍏舵€ц唱(zh矛)銆�

4锛� Hilbert绌洪枔鐨勫畾缇�锛汬ilbert绌洪枔涓婄殑姝ｈ(gu墨)姝ｄ氦鍩�锛屾瑕�(gu墨)姝ｄ氦鍒嗚В锛�

5锛� 鎺屾彙骞剁啛绶撮亱(y霉n)鐢˙essel涓嶇瓑寮�銆丼chwarz涓嶇瓑寮忓強Parseval鍏紡銆�

6锛� 鎺屾彙鍙垎Hilbert绌洪枔鐨勭祼(ji茅)妲�(g貌u)銆�

7锛� 鎺屾彙灏勫奖瀹氱悊锛岀悊瑙ｅ叾娑电京锛屽苟鑳藉姞浠ユ噳(y墨ng)鐢�锛涙帉鎻�琛ㄧ従(xi脿n)瀹氱悊锛孒ilbert绌洪枔涓婄殑绶氭€ф硾鍑界殑琛ㄧず銆�

8锛� Hilbert鍏辫粵绠楀瓙鐨勫畾缇�銆佹€ц唱(zh矛)鍙婂叾琛ㄧず锛涘彲鍒咹ilbert绌洪枔涓婃湁鐣岀窔鎬х畻瀛愮殑鐭╅櫍琛ㄩ仈(d谩)寮忋€�

锛堜笁锛塀anach绌洪枔鍙夿anach绌洪枔涓婄殑鏈夌晫绶氭€х畻瀛�

1. Banach绌洪枔涓婄殑鏈夌晫绶氭€х畻瀛愬畾缇�锛涚畻瀛愯寖鏁�(sh霉)鐨勮▓绠楋紱鑼冩暩(sh霉)鐨勬瘮杓�銆�

2. 鏈夌晫绶氭€х畻瀛愮┖闁�鐨勬€ц唱(zh矛)銆�

3. 绠楀瓙鐨勯€�锛岄€嗙畻瀛愬瓨鍦ㄣ€侀€ｇ簩(x霉)鐨勬浠�锛涘埄鐢ㄩ€嗙畻瀛愯В姹轰竴浜涚⿳鍒嗘柟绋嬬瓑鏂归潰鐨勫(sh铆)闅涘晱椤�銆�

4. Hahn-Banach瀹氱悊锛涙摯(ku貌)寮靛畾鐞嗙殑骞剧ó琛ㄧ従(xi脿n)褰㈠紡锛屽Banach鎿�(ku貌)寮靛畾鐞�銆丅ohnenblust-Sobczyk瀹氱悊绛�銆�

5. Hahn-Banach瀹氱悊鐨勪竴浜涙帹璜栵紝楂旂従(xi脿n)鐨勪笉鍚屽伌(c猫)闈㈢殑Hahn-Banach瀹氱悊鐨勫叿楂旇〃鐝�(xi脿n)褰㈠紡锛汬ahn-Banach瀹氱悊鐨勫咕浣曞舰寮�銆侶ahn-Banach瀹氱悊鍦ㄧ悊璜栧強瀵�(sh铆)闅涗笂鐨勬噳(y墨ng)鐢ㄣ€�

6. 鍒嗛洟瀹氱悊锛屽強鍏惰垏Hahn-Banach瀹氱悊涔嬮枔鐨勯棞(gu膩n)绯�銆�

7. Baire缍卞畾鐞嗭紱绗竴缍遍泦銆佺浜岀侗闆嗙殑瀹氱京鑸囧垎椤�銆�

8. 涓€鑷存湁鐣屽師鐞嗭紙鍏遍炒瀹氱悊锛�锛涢枊鏄犲皠瀹氱悊锛汢anach閫嗙畻瀛愬畾鐞嗭紱闁夊湒褰㈠畾鐞嗕互鍙婂畠鍊戠殑鎳�(y墨ng)鐢�銆�

9. 灏嶅伓绌洪枔鐨勫畾缇�锛屽咕鍊嬪叿楂旂┖闁撲笂鐨勫皪鍋剁┖闁撳強瀹冨€戠殑閫ｇ簩(x霉)娉涘嚱褰㈠紡锛屽

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10. 浜屾灏嶅伓銆佸吀鍨嬫槧灏�銆佽嚜鍙嶇┖闁撶殑瀹氱京锛涙湁闄愮董璩﹁寖绶氭€х┖闁�銆�銆丠ilbert绌洪枔鐨勮嚜鍙嶆€ц唱(zh矛)銆備簡瑙ｅ父瑕嬬殑涓嶆槸鑷弽绌洪枔鐨勪緥瀛�銆�

11. Banach鍏辫粵绠楀瓙鐨勫畾缇�銆佹€ц唱(zh矛)鍙婂叾鐭╅櫍琛ㄧず銆�

12. 绠楀瓙鐨勫€煎煙銆侀浂绌洪枔銆佸晢绌洪枔鐨勫畾缇╄垏瀹冨€戜箣闁撶殑闂�(gu膩n)绯�銆�

锛堝洓锛夋湁鐣岀窔鎬х畻瀛愯瓬璜�

1. 鏈夌晫绶氭€х畻瀛愮殑闋�(y霉)瑙ｅ紡鑸囪瓬鐨勫畾缇╁強鍏惰▓绠�銆�

2. 鎺屾彙璀滃崐寰戝叕寮忥紝鎳�(y墨ng)鐢ㄥ叕寮忚В姹哄晱椤�銆�

3. 灏勫奖绠楀瓙鐨勫畾缇�锛涙湁鐣岀窔鎬х畻瀛愮殑涓嶈畩瀛愮┖闁撹垏绱勫寲瀛愮┖闁擄紱F.Riesz绌洪枔鍒嗚В瀹氱悊銆�

4. 绶婄畻瀛愮殑瀹氱京鍙婂叾鎬ц唱(zh矛)锛涚穵绠楀瓙鐨勫(sh铆)渚�锛涚穵绠楀瓙鑸囩悊鎯崇殑闂�(gu膩n)绯�銆�

5. Riesz-Schauder鐞嗚珫锛欶.Riesz瀹氱悊锛涘叐鎿囦竴瀹氱悊锛汧redholm浜ゆ浛瀹氱悊绛夊畾鐞嗗収(n猫i)瀹硅垏鎳�(y墨ng)鐢ㄣ€�

6. 鏈夌晫鑷即绠楀瓙鐨勫熀鏈€ц唱(zh矛)锛涚穵鑷即绠楀瓙鐨勫畾缇╄垏鎬ц唱(zh矛)锛涢厜绠楀瓙鐨勫畾缇╄垏鎬ц唱(zh矛)銆�

7. 鏈夌晫鑷即绠楀瓙鐨勮瓬娓害锛岃瓬鍒嗚В瀹氱悊鑸囧嚱鏁�(sh霉)婕旂畻銆�

鍏嶈铂(z茅)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�(di菐n)锛岃垏鏈恫(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(sh铆)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(sh铆)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€鑰呭儏浣滃弮鑰冿紝骞惰珛鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�