姝¤繋瑷晱(w猫n)鑰冪爺绉樼睄鑰冪爺缍�(w菐ng)!    鐮旂┒鐢熸嫑鐢熶俊鎭恫(w菐ng)    鑰冨崥鐪熼涓嬭級    鑰冪爺鐪熼涓嬭級    鍏ㄧ珯鏂囩珷绱㈠紩
鏂囩珷鎼滅储
   
  楂樼礆(j铆)鎼滅储   

 鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 鑰冪爺绉樼睄鑰冪爺缍�(w菐ng) >> 鏂囩珷涓績 >> 灏堟キ(y猫)瑾� >> 姝f枃  2018骞存矆闄�(y谩ng)宸ユキ(y猫)澶у(xu茅)娉涘嚱鍒嗘瀽鍔犺│鑰冪爺澶х侗鍔犺│澶х侗

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鑰冭│绉戠洰鍚嶇ū: 娉涘嚱鍒嗘瀽
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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▓(j矛)绠楁柟娉�銆�
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8锛� 澹撶府鏄犲皠瀹氱京锛屾帉鎻″绺槧璞″師鐞嗭紝骞惰兘鐔熺反鐨勬噳(y墨ng)鐢ㄥ畾鐞嗚В姹哄晱(w猫n)椤�銆備簡瑙e绺槧璞″師鐞�
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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�(ji脿n)璩﹁寖绶氭€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� ],[,
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4锛� Hilbert 绌洪枔鐨勫畾缇╋紱Hilbert 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� Bessel 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 RieszcheteFr ?
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琛ㄧ従(xi脿n)瀹氱悊锛孒ilbert
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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� Hilbert 绌洪枔涓婃湁鐣岀窔鎬х畻瀛愮殑鐭╅櫍琛ㄩ仈(d谩)
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锛堜笁锛塀anach 绌洪枔鍙� Banach 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▓(j矛)绠�锛涜寖鏁�(sh霉)鐨勬瘮杓�銆�
2. 鏈夌晫绶氭€х畻瀛愮┖闁� ),( YXL 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(w猫n)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�
Hahn-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)绯汇€�
7. Baire 缍卞畾鐞�锛涚涓€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(k膩i)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)
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9. 灏�(du矛)鍋剁┖闁撶殑瀹氱京锛屽咕鍊�(g猫)鍏烽珨绌洪枔涓婄殑灏�(du矛)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�(du矛)鍋�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� )1](,[ ??? pbaL
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Hilbert 绌洪枔鐨勮嚜鍙嶆€ц唱(zh矛)銆備簡瑙e父瑕�(ji脿n)鐨勪笉鏄嚜鍙嶇┖闁撶殑渚嬪瓙銆�
11. Banach 鍏辫粵绠楀瓙鐨勫畾缇┿€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▓(j矛)绠�銆�
2. 鎺屾彙璀滃崐寰戝叕寮�锛屾噳(y墨ng)鐢ㄥ叕寮忚В姹哄晱(w猫n)椤�銆�
3. 灏勫奖绠楀瓙鐨勫畾缇╋紱鏈夌晫绶氭€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(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�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�(c猫)搴�锛岃瓬鍒嗚В瀹氱悊鑸囧嚱鏁�(sh霉)婕旂畻銆�

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  • 涓婁竴绡囨枃绔狅細

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