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
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瑙g殑瀛樺湪鍞竴鎬у畾鐞�銆佸欢鎷撳畾鐞�銆佽В灏�(du矛)鍒濆€肩殑閫g簩(x霉)渚濊炒鎬у拰鍙井鎬у畾鐞嗕互鍙婃墍娑夊強姒傚康
鐨勬簴(zh菙n)纰虹悊瑙o紝瑙g殑瀛樺湪鍞竴鎬у畾鐞嗙殑瑭崇窗(x矛)璀夋槑銆�
鏁欏(xu茅)鍏�(n猫i)瀹�
绗竴绡€(ji茅) 瑙g殑瀛樺湪鎬ц垏鍞竴鎬у畾鐞�
寮曢€�(j矛n)骞惰┏绱�(x矛)璀夋槑瑙g殑瀛樺湪鍞竴鎬у畾鐞�锛涗緷鎿�(j霉)鍏烽珨渚嬪瓙灏�(du矛)瀹氱悊鐨勬浠跺仛瑭崇窗(x矛)瑾�(shu艒)鏄�銆�
绗簩绡€(ji茅) 瑙g殑寤跺睍
浠嬬垂骞惰瓑鏄庤В鐨勫欢灞曞畾鐞�锛岀ず渚嬭(shu艒)鏄庤┎瀹氱悊鐨勬浠�锛涗粙绱圭涓€姣旇純瀹氱悊銆�
绗笁绡€(ji茅) 瑙e皪(du矛)鍒濆€肩殑閫g簩(x霉)渚濊炒鎬�
浠嬬垂骞惰瓑鏄庤В灏�(du矛)鍒濆€肩殑閫g簩(x霉)渚濊炒鎬у畾鐞�銆�
绗洓绡€(ji茅) 瑙e皪(du矛)鍒濆€肩殑鍙井鎬�
浠嬬垂骞惰瓑鏄庤В灏�(du矛)鍒濆€肩殑鍙井鎬у畾鐞嗐€�
鑰冩牳瑕佹眰
閲嶉粸(di菐n)鎺屾彙瑙g殑瀛樺湪鍞竴鎬у畾鐞�銆佸欢鎷撳畾鐞嗙殑鍏�(n猫i)瀹逛互鍙婅В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞嗙殑璀夋槑鎬濇兂锛�
鐔熺反鎺屾彙 Picard 閫艰繎鍒�銆丩ipschits 姊濅欢鍜屽欢鎷撴蹇点€�
绗笁绔� 绶氭€у井鍒嗘柟绋�
鑰冭│瑕侀粸(di菐n)
婧�(zh菙n)纰虹悊瑙g窔鎬у井鍒嗘柟绋嬬殑涓€鑸悊璜�锛涚啛绶存帉鎻� Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曞拰甯哥郴鏁�(sh霉)绶�
鎬у井鍒嗘柟绋嬬殑鐗瑰緛鏍规硶銆佹瘮杓冪郴鏁�(sh霉)娉曘€丩aplace 璁婃彌锛涚悊瑙f尟鍕�(d貌ng)鐝�(xi脿n)璞�銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 绶氭€ф柟绋嬬殑涓€鑸€ц唱(zh矛)
绶氭€у井鍒嗘柟绋嬬殑瑙g殑瀛樺湪鍞竴鎬у畾鐞嗗強绶氭€у井鍒嗙畻瀛愮殑鎬ц唱(zh矛)銆�
绗簩绡€(ji茅) n 闅庣窔鎬ч綂娆″井鍒嗘柟绋�
寤虹珛榻婃绶氭€у井鍒嗘柟绋嬬殑涓€鑸悊璜�锛屽緱鍒伴€氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛岃瓑鏄� Liouville 鍏紡骞舵噳(y墨ng)鐢ㄥ埌
2 闅庡井鍒嗘柟绋�銆�
绗笁绡€(ji茅) n 闅庣窔鎬ч潪榻婃鏂圭▼
n 闅庣窔鎬ч潪榻婃鏂圭▼鐨勯€氳В绲�(ji茅)妲�(g貌u)瀹氱悊鑸囧父鏁�(sh霉)璁婃槗娉�銆�
绗洓绡€(ji茅) n 闅庡父绯绘暩(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬭В娉�
鐢ㄧ壒寰佹牴娉曡В甯哥郴鏁�(sh霉)绶氭€ч綂娆″井鍒嗘柟绋嬬殑鍩烘湰姝ラ銆佺悊璜栬瓑鏄�銆佸吀鍨嬬ず渚�銆�
绗簲绡€(ji茅) n 闅庡父绯绘暩(sh霉)绶氭€ч潪榻婃寰垎鏂圭▼瑙f硶
姣旇純绯绘暩(sh霉)娉曠殑寤虹珛銆佺悊璜栬瓑鏄�銆佸吀鍨嬬ず渚�銆�
绗叚绡€(ji茅) Laplace 璁婃彌
浠嬬垂 Laplace 璁婃彌浠ュ強濡備綍鎳�(y墨ng)鐢� Laplace 璁婃彌姹傝В涓€浜涘父绯绘暩(sh霉)绶氭€ч潪榻婃寰垎鏂圭▼鐨�
Cauchy 鍟�(w猫n)椤屻€�
绗竷绡€(ji茅) 2 闅庡父绯绘暩(sh霉)绶氭€ф柟绋嬭垏鎸嫊(d貌ng)鐝�(xi脿n)璞�
渚濇摎(j霉)绶氭€у井鍒嗘柟绋嬬殑瑙g殑琛ㄧず瑙i噵鎸嫊(d貌ng)鐝�(xi脿n)璞�銆�
鑰冩牳瑕佹眰
婧�(zh菙n)纰虹悊瑙g窔鎬у井鍒嗘柟绋嬬殑涓€鑸悊璜�锛涚啛绶存帉鎻� Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉�銆佺壒寰佹牴娉�銆�
姣旇純绯绘暩(sh霉)娉曞拰 Laplace 璁婃彌锛涜兘澶犱緷鎿�(j霉)瑙g殑涓€鑸〃绀鸿◣璜栬В鐨勪竴浜涘爆鎬�銆�
绗洓绔� 绶氭€у井鍒嗘柟绋嬬祫
鑰冭│瑕侀粸(di菐n)
婧�(zh菙n)纰虹悊瑙g窔鎬у井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛涜兘澶犵啛绶存帉鎻� Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉�銆佸父
绯绘暩(sh霉)绶氭€у井鍒嗘柟绋嬬殑鐗瑰緛鏍规硶鍜岀啊(ji菐n)鍠殑闈為綂娆℃柟绋嬬殑瑙f硶銆�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 涓€闅庡井鍒嗘柟绋嬬祫
涓€闅庡井鍒嗘柟绋嬬祫鍒濆€煎晱(w猫n)椤岃В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞�銆�
绗簩绡€(ji茅) 绶氭€у井鍒嗘柟绋嬬祫鐨勪竴鑸蹇�
涓€闅庣窔鎬у井鍒嗘柟绋嬬祫鍒濆€煎晱(w猫n)椤岃В鐨勫瓨鍦ㄥ敮涓€鎬у畾鐞嗐€�
娉細绗竴绡€(ji茅)鑸囩浜岀瘈(ji茅)鍏� 2 瀛�(xu茅)鏅�(sh铆)
绗笁绡€(ji茅) 绶氭€ч綂娆″井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�
寤虹珛绶氭€ч綂娆″井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛屽緱鍒伴€氳В绲�(ji茅)妲�(g貌u)瀹氱悊锛岃瓑鏄� Liouville 鍏紡銆�
绗洓绡€(ji茅) 绶氭€ч潪榻婃寰垎鏂圭▼绲勭殑涓€鑸悊璜�
绶氭€ч潪榻婃寰垎鏂圭▼绲勭殑涓€鑸悊璜栧拰甯告暩(sh霉)璁婃槗娉曘€�
绗簲绡€(ji茅) 甯哥郴鏁�(sh霉)绶氭€у井鍒嗘柟绋嬬祫鐨勮В娉�
鐗瑰緛鏍规硶鈥旂悊璜栬瓑鏄庤垏鏂规硶鐨勭啛绶存噳(y墨ng)鐢�锛涚啊(ji菐n)鍠殑闈為綂娆℃柟绋嬬殑瑙f硶銆�
鑰冩牳瑕佹眰
婧�(zh菙n)纰虹悊瑙g窔鎬у井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜�锛涚啛绶存帉鎻� Liouville 鍏紡銆佸父鏁�(sh霉)璁婃槗娉曞拰鐗瑰緛鏍�
娉�锛涜兘澶犱緷鎿�(j霉)瑙g殑涓€鑸〃绀鸿◣璜栬В鐨勪竴浜涘爆鎬�銆�
绗簲绔� 瀹氭€ц垏绌�(w臎n)瀹氭€ф蹇�
鑰冭│瑕侀粸(di菐n)
浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炲強鍏堕檮杩戠殑杌岀窔鍒嗗竷锛涙サ闄愮挵(hu谩n)鐨勫畾缇╄垏绀轰緥锛涚┅(w臎n)瀹氭€ф蹇�
鍙婂叾鍒ゅ畾瀹氱悊锛屽垎鍒ユ噳(y墨ng)鐢ㄧ┅(w臎n)瀹氭€ф蹇�銆佺窔鎬у寲绯荤当(t菕ng)鐨勭壒寰佸€�銆丩iapunov 绗簩鏂规硶瑷庤珫鑷不
绯荤当(t菕ng)鐨勮В鐨勭┅(w臎n)瀹氭€с€�
鑰冭│鍏�(n猫i)瀹�
绗竴绡€(ji茅) 鐩稿钩闈綔鍦� 鍠摵
鑷不绯荤当(t菕ng)鍙婂叾杌岀窔鐨勫垎椤炶垏鎬ц唱(zh矛)銆�
绗簩绡€(ji茅) 鍒濈瓑濂囬粸(di菐n)闄勮繎鐨勮粚绶氬垎甯�
浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炩€旂祼(ji茅)榛�(di菐n)銆侀瀺榛�(di菐n)銆佺劍榛�(di菐n)銆佷腑蹇冨強鍏堕檮杩戠殑杌岀窔鍒嗗竷銆�
绗笁绡€(ji茅) 妤甸檺鐠�(hu谩n)鑸変緥
妤甸檺鐠�(hu谩n)鐨勫畾缇╄垏绀轰緥銆�
绗洓绡€(ji茅) 绌�(w臎n)瀹氭€ф蹇�
绌�(w臎n)瀹氭€ф蹇�銆佸垽瀹氬畾鐞嗗拰鍒ゅ畾鏂规硶锛岃憲閲� Liapunov 绗簩鏂规硶銆�
鑰冩牳瑕佹眰
閲嶉粸(di菐n)鎺屾彙浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炲強鍏堕檮杩戠殑杌岀窔鍒嗗竷锛涚悊瑙g┅(w臎n)瀹氭€ф蹇靛強鍏跺垽瀹�
瀹氱悊锛屾渻(hu矛)鎳�(y墨ng)鐢ㄧ┅(w臎n)瀹氭€ф蹇�銆佺窔鎬у寲绯荤当(t菕ng)鐨勭壒寰佸€笺€丩iapunov 绗簩鏂规硶瑷庤珫鑷不绯荤当(t菕ng)鐨勮В鐨�
绌�(w臎n)瀹氭€�銆�
浜�銆� 鍙冭€冩浉(sh奴)鐩�
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4銆� 鍦�(gu贸)瀹舵暀鑲插鍝℃渻(hu矛)甯寖鏁欒偛鍙�锛屻€婃櫘閫氶珮搴﹀斧鑼冨(xu茅)鏍℃暩(sh霉)瀛�(xu茅)鏁欒偛灏堟キ(y猫)锛堟湰绉戯級鏁欒偛鏁欏(xu茅)鍩烘湰
瑕佹眰锛堣│琛岋級銆�锛岄閮藉斧鑼冨ぇ瀛�(xu茅)鍑虹増绀�锛�1994銆�
娉涘嚱鍒嗘瀽
绗竴绔� 搴﹂噺绌洪枔鑸囩窔鎬ц肠鑼冪┖闁�
鑰冭│瑕侀粸(di菐n)锛�
搴﹂噺绌洪枔鐨勬蹇�锛屼緥瀛�锛涘害閲忕┖闁撲腑鐨勬敹鏂傛€ц垏閫g簩(x霉)鎬�锛涚瀵嗘€�锛涘彲鍒嗘€�锛汣auchy 鍒�
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鐨勬蹇点€�
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R 锛涢€g簩(x霉)鍑芥暩(sh霉)绌洪枔 ],[ baC 锛涙暩(sh霉)鍒楃┖闁�
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绗笁绡€(ji茅) 閫g簩(x霉)鏄犲皠
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绗洓绡€(ji茅) Cauchy 榛�(di菐n)鍒楄垏瀹屽倷搴﹂噺绌洪枔
搴﹂噺绌洪枔涓� Cauchy 榛�(di菐n)鍒楃殑姒傚康锛涘畬鍌欏害閲忕┖闁撶殑瀹氱京锛涘畬鍌欏害閲忕┖闁撹垏涓嶅畬鍌欏害閲忕┖
闁撶殑鍚勯渚嬪瓙锛涘害閲忕┖闁撻枆瀛愮┖闁撶殑瀹屽倷鎬�銆�
绗簲绡€(ji茅) 搴﹂噺绌洪枔鐨勫畬鍌欏寲
绛夎窛鍚屾(g貌u)锛涘害閲忕┖闁撶殑瀹屽倷鍖栧畾鐞�锛�
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绗竷绡€(ji茅) 绶氭€х┖闁�
鏈瘈(ji茅)鍏�(n猫i)瀹圭偤绶氭€х┖闁撶殑鍩烘湰姒傚康銆傚洜?q奴)W鐢熷凡鍦ㄩ珮绛変唬鏁�(sh霉)瑾茬▼涓(xu茅)閬�(gu貌)鏈夐檺缍┖闁撶殑鏈夐棞(gu膩n)
鍏�(n猫i)瀹�锛屾晠鍙渶绨�(ji菐n)瑕佸洖椤у苟寮�(qi谩ng)瑾�(di脿o)鐒�(w煤)闄愮董绶氭€х┖闁撶殑鐗瑰緛鍗冲彲銆�
绗叓绡€(ji茅) 绶氭€ц肠鑼冪┖闁撳拰 Banach 绌洪枔
鑼冩暩(sh霉)锛岀窔鎬ц肠鑼冪┖闁撳拰 Banach 绌洪枔鐨勬蹇�锛涗緷鑼冩暩(sh霉)鏀舵杺锛� n
R 绌洪枔锛� ],[ baC 绌洪枔锛� ?
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鑰冩牳瑕佹眰锛�
鎺屾彙搴﹂噺绌洪枔锛岀窔鎬ц肠鑼冪┖闁撳拰 Banach 绌洪枔鐨勬蹇靛拰鎬ц唱(zh矛)锛涙帉鎻℃槧灏勯€g簩(x霉)鎬�锛屽害閲忕┖
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R 绌洪枔锛� ],[ baC 绌洪枔锛� ?
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l 绌洪枔锛� ],[ baL
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闁�锛涢€忓竟鐞嗚В澹撶府鏄犲儚鍘熺悊鍙婂叾绨�(ji菐n)鍠噳(y墨ng)鐢�銆傝兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�
绗簩绔� 绶氭€ф湁鐣岀畻瀛愬拰绶氭€ч€g簩(x霉)娉涘嚱
鑰冭│瑕侀粸(di菐n)锛�
绶氭€ф湁鐣岀畻瀛�锛岀窔鎬ч€g簩(x霉)娉涘嚱锛岀窔鎬х畻瀛愮┖闁�锛屽叡杌涚┖闁撱€�
鑰冭│鍏�(n猫i)瀹癸細
绗竴绡€(ji茅) 绶氭€ф湁鐣岀畻瀛愯垏绶氭€ч€g簩(x霉)娉涘嚱
绶氭€ф湁鐣岀畻瀛愯垏绶氭€ч€g簩(x霉)娉涘嚱鐨勬蹇�锛屼緥瀛愶紝鏈夌晫鑸囬€g簩(x霉)鐨勭瓑鍍�(ji脿)鎬�锛岀窔鎬ф湁鐣岀畻瀛愰浂绌�
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绗簩绡€(ji茅) 绶氭€х畻瀛愮┖闁撳拰鍏辫粵绌洪枔
绶氭€х畻瀛愮┖闁撶殑绲�(ji茅)妲�(g貌u)鍙婂叾瀹屽倷鎬э紝鍏辫粵绌洪枔锛屼繚璺濈畻瀛�锛屽悓妲�(g貌u)鏄犵収锛屽悓妲�(g貌u)锛屼竴浜涘叿楂旂┖
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鎺屾彙绶氭€ф湁鐣岀畻瀛�锛岀窔鎬ч€g簩(x霉)娉涘嚱锛屾湁鐣屾€�锛岄€g簩(x霉)鎬�锛岀畻瀛愯寖鏁�(sh霉)锛屽叡杌涚┖闁�锛屼繚璺濈畻瀛�锛�
鍚屾(g貌u)鏄犵収锛屽悓妲�(g貌u)绛夊熀鏈蹇�锛涙帉鎻℃湁鐣岃垏閫g簩(x霉)鐨勭瓑鍍�(ji脿)鎬у畾鐞嗭紝鍩烘湰瀹氱悊锛涜兘澶犺▓(j矛)绠楃啊(ji菐n)鍠殑绠�
瀛愯寖鏁�(sh霉)鍜屼竴浜涘叿楂旂┖闁撶殑鍏辫粵绌洪枔銆傝兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤屻€�
绗笁绔� 鍏�(n猫i)绌嶇┖闁撳拰 Hilbert 绌洪枔
鑰冭│瑕侀粸(di菐n)锛�
鍏�(n猫i)绌嶇┖闁�锛屾姇褰卞畾鐞�锛孒ilbert 绌洪枔锛屽氨鑼冪洿浜ょ郴锛孒ilbert 绌洪枔涓婄窔鎬ч€g簩(x霉)娉涘嚱鐨勮〃绀�銆�
鑰冭│鍏�(n猫i)瀹癸細
绗竴绡€(ji茅) 鍏�(n猫i)绌嶇┖闁撶殑鍩烘湰姒傚康
鍏�(n猫i)绌嶇┖闁撹垏 Hilbert 绌洪枔鐨勫畾缇�锛屽钩琛屽洓閭婂舰鍏紡锛屽収(n猫i)绌嶇┖闁撶殑鍒ゅ畾銆�
绗簩绡€(ji茅) 鎶曞奖瀹氱悊
榛�(di菐n)鍒伴泦鍚堢殑璺濋洟锛屽嚫闆嗭紝妤靛皬鍖栧悜閲忓畾鐞�锛岄泦鍚堢殑姝d氦锛孒ilbert 绌洪枔鐨勬浜ゅ垎瑙�锛屾姇
褰辩畻瀛愬強鍏舵€ц唱(zh矛)銆�
绗笁绡€(ji茅) Hilbert 绌洪枔涓殑灏辫寖鐩翠氦绯�
灏辫寖鐩翠氦绯伙紝F(xi脿n)ourier 绯绘暩(sh霉)闆�锛孊essel 涓嶇瓑寮�锛孭arseval 鎭掔瓑寮忥紝瀹屽叏灏辫寖鐩翠氦绯荤殑瀹氱京
鑸囧垽瀹�, Fourier 灞曞紡锛孏ram-Schmidt 姝d氦鍖栭亷(gu貌)绋�锛孒ilbert 绌洪枔鐨勫悓妲�(g貌u)銆�
绗洓绡€(ji茅) Hilbert 绌洪枔涓婄殑绶氭€ч€g簩(x霉)娉涘嚱
Riesz 琛ㄧず瀹氱悊锛屽叡杌涚畻瀛愬強鍏舵€ц唱(zh矛)銆�
绗簲绡€(ji茅) 鑷即绠楀瓙銆� 閰夌畻瀛愬拰姝e父绠楀瓙
鑷即绠楀瓙銆� 閰夌畻瀛愬拰姝e父绠楀瓙鐨勫熀鏈蹇佃垏绨�(ji菐n)鍠€ц唱(zh矛)銆�
鑰冩牳瑕佹眰锛�
鎺屾彙鍏�(n猫i)绌嶇┖闁擄紝Hilbert 绌洪枔锛屽钩琛屽洓閭婂舰鍏紡锛屽氨鑼冪洿浜ょ郴锛孊essel 涓嶇瓑寮�锛孭arseval
鎭掔瓑寮�锛孎(xi脿n)ourier 灞曞紡锛屾姇褰辩畻瀛�锛屽叡杌涚畻瀛愶紝鑷即绠楀瓙锛岄厜绠楀瓙鍜屾甯哥畻瀛愮瓑鍩烘湰姒傚康锛�
鎺屾彙妤靛皬鍖栧悜閲忓畾鐞�锛屾姇褰卞畾鐞�锛屽畬鍏ㄥ氨鑼冪洿浜ょ郴鐨勫垽瀹氬畾鐞�, Riesz 琛ㄧず瀹氱悊绛夊熀鏈畾鐞�
鐨勫収(n猫i)瀹硅垏璀夋槑锛涜兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�
绗洓绔� Banach 绌洪枔涓殑鍩烘湰瀹氱悊
鑰冭│瑕侀粸(di菐n)锛�
Hahn-Banach 寤舵嫇瀹氱悊锛孯iesz 琛ㄧず瀹氱悊锛岀窔鎬ц肠鑼冪┖闁撲腑鐨勫叡杌涚畻瀛愶紝
绗竴绡€(ji茅) 娉涘嚱寤舵嫇瀹氱悊
娆$窔鎬ф硾鍑�锛孒ahn-Banach 娉涘嚱寤舵嫇瀹氱悊鐨勫(sh铆)褰㈠紡銆佸京(f霉)褰㈠紡鍙婂叾鎺ㄨ珫銆�
绗簩绡€(ji茅) ],[ baC 鐨勫叡杌涚┖闁�銆丷iesz 琛ㄧず瀹氱悊
绗笁绡€(ji茅) 鍏辫粵绠楀瓙
绗洓绡€(ji茅) 绶氭€ц肠鑼冪┖闁撲腑鍏辫粵绠楀瓙鐨勫畾缇╁強鎬ц唱(zh矛)銆�
绗簲绡€(ji茅) 缍卞畾鐞嗗拰涓€鑷存湁鐣屾€у畾鐞�
绗竴缍遍泦锛岀浜岀侗闆�锛孊aire 缍卞畾鐞�, 涓€鑷存湁鐣屾€у畾鐞嗗挤(qi谩ng)鏀舵杺銆佸急鏀舵杺鍜屼竴鑷存敹鏂�
寮�(qi谩ng)鏀舵杺銆佸急鏀舵杺銆佸急*鏀舵杺鍜屼竴鑷存敹鏂傜殑瀹氱京锛屼緥瀛愶紝鐩镐簰闂�(gu膩n)绯伙紝寮�(qi谩ng)鏀舵杺鐨勫厖瑕佹浠�銆�
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绗竷绡€(ji茅) 闁夊湒璞″畾鐞�
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鑰冩牳瑕佹眰锛�
鎺屾彙鏈珷娑夊強鍒扮殑鎵€鏈夊熀鏈蹇�锛屽熀鏈畾鐞�锛涚敱浜� Hahn-Banach 寤舵嫇瀹氱悊锛孯iesz 琛ㄧず
瀹氱悊锛孊aire 缍卞畾鐞�锛岄€嗙畻瀛愬畾鐞�锛岄枆鍦栬薄瀹氱悊鏄硾鍑藉垎鏋愬熀绀�(ch菙)鐞嗚珫鐨勪富瑕佹(g貌u)鎴愰儴鍒�锛岃姹�
鐔熺反鎺屾彙閫欎簺鍏�(n猫i)瀹�锛涜兘鐛�(d煤)绔嬭В绛斿熀鏈殑缈�(x铆)椤�銆�
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涓�銆佸弮鑰冩浉(sh奴)鐩�
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