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鍜� Leibniz 鍒ゅ垾娉�锛岀禃灏嶆敹鏂傝垏姊濅欢鏀舵杺锛屾煰瑗挎敹鏂傚師鐞�锛孉bel 璁婃彌浠ュ強闂滀簬涓€鑸暩(sh霉)闋呯礆鏁�(sh霉)
鐨� Abel 闃胯矟鐖惧垽鍒ユ硶鍜� Dirichlet 鍒ゅ垾娉�,绱氭暩(sh霉)鐨勯噸鎺掑晱椤屽強涔樼⿳鍟忛銆�
2銆� 鑰冭│瑕佹眰
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鐢ㄦ闋呯礆鏁�(sh霉)鏀舵杺鐨勫垽鍒ユ硶(姣旇純鍒ゅ垾娉�銆佹瘮鍊煎垽鍒ユ硶銆佹牴寮忓垽鍒ユ硶銆佹媺闃挎瘮鍒ゅ垾娉�銆佺⿳鍒嗗垽
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鐨勬€ц唱锛孋auchy 鏀舵杺婧栧墖锛屾瘮杓冨垽鍒ユ硶锛岀⿳鍒嗙浜屼腑鍊煎畾鐞嗭紝Abel 闃胯矟鐖惧垽鍒ユ硶鍜� Dirichlet
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绌嶅垎鐨勬€ц唱銆佺⿳鍒嗘敹鏂傜殑姣旇純鍒ゅ垾娉�銆丄bel 闃胯矟鐖惧垽鍒ユ硶鍜� Dirichlet 鍒ゅ垾娉曪紝鐞嗚В Cauchy
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閲嶉粸锛氱⿳鍒嗘敹鏂傜殑姣旇純鍒ゅ垾娉�锛孉bel 闃胯矟鐖惧垽鍒ユ硶鍜� Dirichlet 鍒ゅ垾娉�銆�
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妤甸檺鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(閫ｇ簩(x霉)鎬�銆佸彲绌嶆€�銆佸彲寰€�)锛涘嚱鏁�(sh霉)闋呯礆鏁�(sh霉)涓€鑷存敹鏂傛€ф蹇�锛屼竴鑷存敹鏂傜殑
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鍒ゅ垾娉曘€丄bel 鍒ゅ垾娉�銆丏irichlet 鍒ゅ垾娉�)锛屼竴鑷存敹鏂傜殑鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(閫ｇ簩(x霉)
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鏂傛€ф蹇�銆佷竴鑷存敹鏂傜殑 Cauchy 鏀舵杺婧栧墖銆佸嚱鏁�(sh霉)闋呯礆鏁�(sh霉)涓€鑷存敹鏂傜殑蹇呰姊濅欢锛岃兘澶犻亱鐢ㄥ嚱鏁�(sh霉)
闋呯礆鏁�(sh霉)涓€鑷存敹鏂傛€х殑鍒ゅ垾娉� (M 鍒ゅ垾娉�銆丄bel 鍒ゅ垾娉�銆丏irichlet 鍒ゅ垾娉�)鍒ゆ柗绱氭暩(sh霉)鐨勪竴鑷存敹
鏂傛€�锛岀悊瑙ｄ竴鑷存敹鏂傜殑鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(閫ｇ簩(x霉)鎬�銆佸彲绌嶆€�銆佸彲寰€�)骞惰兘澶犳
纰烘噳鐢�銆�
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閲嶉粸锛氫竴鑷存敹鏂傛€х殑鍒ゅ垾娉� (M 鍒ゅ垾娉曘€丄bel 鍒ゅ垾娉�銆丏irichlet 鍒ゅ垾娉�)锛屼竴鑷存敹鏂傜殑
鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(閫ｇ簩(x霉)鎬�銆佸彲绌嶆€с€佸彲寰€�)銆�
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绗崄涓夌珷鍐礆鏁�(sh霉)
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鍐礆鏁�(sh霉)鐨勬敹鏂傚煙鍜屾敹鏂傚崐寰�锛孉bel 绗竴瀹氱悊鍜岀浜屽畾鐞�锛屽啰绱氭暩(sh霉)鍜屽嚱鏁�(sh霉)鐨勬€ц唱(閫ｇ簩(x霉)鎬с€�
鍙⿳鎬�銆佸彲寰€�)锛屽嚱鏁�(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊銆�
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鍑芥暩(sh霉)鐨勬€ц唱(閫ｇ簩(x霉)鎬с€佸彲绌嶆€�銆佸彲寰€�)銆�
3銆� 閲嶉粸鑸囬洠榛�
閲嶉粸锛氬啰绱氭暩(sh霉)鐨勬敹鏂傚煙鍜屾敹鏂傚崐寰戠殑姹傛硶锛屽啰绱氭暩(sh霉)鎳夌敤锛屽嚱鏁�(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊銆�
闆ｉ粸锛欰bel 绗竴瀹氱悊鍜岀浜屽畾鐞嗭紝鍑芥暩(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊銆�
绗崄鍥涚珷鍌呴噷钁夌礆鏁�(sh霉)
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涓夎鍑芥暩(sh霉)绯伙紝涓夎绱氭暩(sh霉)鐨勬蹇�锛屼互 2? 鐐哄懆鏈熺殑鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)锛孎(xi脿n)ourier 绱氭暩(sh霉)鐨勬敹
鏂傚畾鐞嗭紝鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)灞曢枊娉�銆�
2銆� 鑰冭│瑕佹眰
鐞嗚В涓夎绱氭暩(sh霉)鍜屾浜ゅ嚱鏁�(sh霉)绯荤殑姒傚康锛屾帉鎻� Fourier 绱氭暩(sh霉)鐨勭郴鏁�(sh霉)瑷堢畻鍏紡锛屾渻瀵嚭鍑芥暩(sh霉)鐨�
Fourier 绱氭暩(sh霉)浠ュ強濂囧嚱鏁�(sh霉)銆佸伓鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)灞曢枊寮�锛岀悊瑙� Fourier 绱氭暩(sh霉)鐨勬敹鏂傚畾鐞嗗拰
Riemann-Lebesgue 寮曠悊銆�
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绗崄浜旂珷澶氬厓鍑芥暩(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)
1銆� 鑰冭│鍏�(n猫i)瀹�
骞抽潰榛為泦鐨勬湁闂滄蹇�(鍗€(q奴)鍩�銆佽窛闆�銆佽仛榛�銆侀枊闆嗗拰闁夐泦绛�)锛屼簩缍┖闁撶殑鍩烘湰瀹氱悊(鐭╁舰濂�
瀹氱悊銆佽嚧瀵嗘€у畾鐞嗐€丆auchy 鏀舵杺鍘熺悊銆佹湁闄愯钃嬪畾鐞�)锛屽鍏冨嚱鏁�(sh霉)鐨勬サ闄愬拰閫ｇ簩(x霉)鎬э紝澶氬厓鍑�
鏁�(sh霉)鐨勭疮娆℃サ闄�锛屾湁鐣岄枆鍗€(q奴)鍩熶笂鐨勯€ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(鏈夌晫鎬�銆佹渶鍊兼€�銆佷粙鍊兼€с€佷竴鑷撮€ｇ簩(x霉)鎬�)銆�
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涓婁竴绡囨枃绔狅細 2017骞存捣鍗楀斧鑼冨ぇ瀛稿璁婂嚱鏁�(sh霉)鑰冪爺澶х侗
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鏂囩珷鎼滅储
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