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骞达紱鍧囨彁渚涙敹璨�(f猫i)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
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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
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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焙鍟忛鐨勮兘鍔涖€�
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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┖闁撱€�
3锛� Cauchy搴忓垪鐨勬€ц唱(zh矛)锛岃窛闆㈢┖闁撶殑瀹屽倷鎬�銆�
4锛� 鍒楃穵闆嗭紝瀹屽叏鏈夌晫闆嗙殑瀹氱京鍙婂畠鍊戜箣闁撶殑闂�(gu膩n)绯�銆�
5锛� 璩﹁寖绶氭€х┖闁撳畾缇�锛涜寖鏁�(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�銆傛帉鎻¢€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氦鍩猴紝姝h(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)鐢紱鎺屾彙 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�銆侀€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闅涘晱椤屻€�
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忋€侶ahn-Banach瀹氱悊鍦ㄧ悊璜栧強瀵﹂殯涓婄殑鎳�(y墨ng)鐢�銆�
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�锛涢枆鍦栧舰瀹氱悊浠ュ強瀹冨€戠殑鎳�(y墨ng)鐢�銆�
9. 灏嶅伓绌洪枔鐨勫畾缇╋紝骞惧€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勩€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愩€�
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)绯汇€�
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�锛汧.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�銆�
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�锛岃珛鑱�(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�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€鑰呭儏浣滃弮鑰冿紝骞惰珛鑷鏍稿鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
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