[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/20778#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/20778","headline":"Pontrjagin Duality-Wikipedia","name":"Pontrjagin Duality-Wikipedia","description":"before-content-x4 Pontrjagin\u4e8c\u91cd\u6027 \u3001Lew Semjonowitsch Pontrjagin\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u3082\u306e\u306f\u3001\u8abf\u548c\u306e\u3068\u308c\u305f\u5206\u6790\u304b\u3089\u306e\u6570\u5b66\u7684\u7528\u8a9e\u3067\u3059\u3002 \u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u30b7\u30a7\u30f3\u30b0\u30eb\u30fc\u30d7\u306f\u3001\u5225\u306e\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u30b7\u30a7\u30b0\u30eb\u30fc\u30d7\u306b\u306a\u308a\u307e\u3059 \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7 \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u304c\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u306b\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u304c\u518d\u3073\u6700\u521d\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u306a\u308b\u3088\u3046\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u307e\u3059\u3002 \u3053\u306e\u69cb\u9020\u306f\u3001\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u306e\u62bd\u8c61\u7684\u306a\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068\u69cb\u9020\u7406\u8ad6\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002 after-content-x4 \u5186\u5f62\u7dda T= { \u3068 \u2208 C; | \u3068 | =","datePublished":"2023-07-18","dateModified":"2023-07-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/612bf4632785fabf466732cfd12723fe3691bc91","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/612bf4632785fabf466732cfd12723fe3691bc91","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/20778","wordCount":8193,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Pontrjagin\u4e8c\u91cd\u6027 \u3001Lew Semjonowitsch Pontrjagin\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u305f\u3082\u306e\u306f\u3001\u8abf\u548c\u306e\u3068\u308c\u305f\u5206\u6790\u304b\u3089\u306e\u6570\u5b66\u7684\u7528\u8a9e\u3067\u3059\u3002\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u30b7\u30a7\u30f3\u30b0\u30eb\u30fc\u30d7\u306f\u3001\u5225\u306e\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u30b7\u30a7\u30b0\u30eb\u30fc\u30d7\u306b\u306a\u308a\u307e\u3059 \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7 \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u304c\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u306b\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u304c\u518d\u3073\u6700\u521d\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u306a\u308b\u3088\u3046\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u69cb\u9020\u306f\u3001\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u306e\u62bd\u8c61\u7684\u306a\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068\u69cb\u9020\u7406\u8ad6\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5186\u5f62\u7dda T= { \u3068 \u2208 C; | \u3068 | = \u521d\u3081 } {displaystyle {mathbb {t}} = {zin {mathbb {c}}; | z | = 1}}} \u30b0\u30eb\u30fc\u30d7\u30ea\u30f3\u30af\u3068\u3057\u3066\u306e\u4e57\u7b97\u3092\u542b\u3080\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3067\u3059\u3002 G\u304c\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u306e\u30b0\u30eb\u30fc\u30d7\u3067\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u306f\u5b9a\u5e38\u30b0\u30eb\u30fc\u30d7\u306e\u540c\u578b\u3068\u547c\u3070\u308c\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 \uff1a g \u2192 T{displaystyle chi\uff1agrightarrow {mathbb {t}}} a \u30ad\u30e3\u30e9\u30af\u30bf\u30fc G. \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7  G^{displaystyle {hat {g}}} g\u304b\u3089G\u304b\u3089\u306e\u3059\u3079\u3066\u306e\u6587\u5b57\u306e\u91cf\u304c\u3042\u308a\u307e\u3059\u3002\u4e57\u7b97\u3067 \uff08 \u30d0\u30c4 de \u03c6 \uff09\uff09 \uff08 a \uff09\uff09 \uff1a= \u30d0\u30c4 \uff08 a \uff09\uff09 \u03c6 \uff08 a \uff09\uff09 {displaystyle\uff08chi cdot psi\uff09\uff08a\uff09\uff1a= chi\uff08a\uff09psi\uff08a\uff09} \u306a\u308a\u307e\u3059 G^{displaystyle {hat {g}}} \u30a2\u30d9\u30eb\u30b0\u30eb\u30fc\u30d7\u306b\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u30b3\u30f3\u30d0\u30fc\u30b8\u30a7\u30f3\u30b9\u306e\u30c8\u30dd\u30ed\u30b8\u3092\u4f5c\u6210\u3057\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4G^{displaystyle {hat {g}}} \u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3001\u3064\u307e\u308aH.\u30c8\u30dd\u30ed\u30b8\u30fc\u304c\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u30c8\u30dd\u30ed\u30b8\u30fc\u30b0\u30eb\u30fc\u30d7\u306b\u3002 \u306f \u30d5\u30a1\u30a4 \uff1a g \u2192 h {displaystyle varphi colon grightarrow h} \u4e00\u5b9a\u306e\u540c\u6027\u611b\u3001\u305d\u3046\u3067\u3059 \u03c6^\uff1a H^\u2192 G^\u3001 \u03c6^\uff08 \u30d0\u30c4 \uff09\uff09 \uff1a= \u30d0\u30c4 \u2218 \u30d5\u30a1\u30a4 {displaystyle {hat {varphi}}\uff1a{hat {h} rightarow \u307e\u305f\u3001\u4e00\u5b9a\u306e\u540c\u6027\u611b\u3082\u3042\u308a\u307e\u3059 \u30d5\u30a1\u30a4 {displaystyle varphi}  \u30c7\u30e5\u30a2\u30eb \u540c\u6027\u611b\u3002 \u6b8b\u308a\u306e\u30af\u30e9\u30b9\u30b0\u30eb\u30fc\u30d7\u306e\u6587\u5b57 Z\/n Z{displaystyle {mathbb {z}}\/n {mathbb {z}}}} \u5f62\u3092\u3057\u3066\u304f\u3060\u3055\u3044 \u03c7m\uff1a Z\/n Z\u2192 T\u3001 \u03c7m\uff08 [ k ] \uff09\uff09 = e2\u03c0ikm\/n{displaystyle chi _ {m}\uff1a{mathbb {z}}\/n {mathbb {z}} rightarrow {mathbb {t}} ,, chi _ {m}\uff08[k]\uff09= e^{2pi ikm\/n}}}}}} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 m \u2208 Z{displaystyle min {mathbb {z}}} \u3002\u9069\u7528\u3055\u308c\u307e\u3059 \u03c7m1= \u03c7m2{displaystyle chi _ {m_ {1}} = chi _ {m_ {2}}}}} \u3001\u6edd m1+ n Z= m2+ n Z{displaystyle m_ {1}+n {mathbb {z}} = m_ {2}+n {mathbb {z}}}}} \u3001 \u3057\u305f\u304c\u3063\u3066 Z\/nZ^\u2245 Z\/n Z{displaystyle {widehat {{mathbb {z}}}\/n {mathbb {z}}}}} cong {mathbb {z}}\/n {mathbb {z}}}}}}}} \u3002 \u306e\u3059\u3079\u3066\u306e\u30ad\u30e3\u30e9\u30af\u30bf\u30fc T{displaystyle {mathbb {t}}} \u5f62\u304c\u3042\u308a\u307e\u3059 \u03c7n\uff08 \u3068 \uff09\uff09 = zn{displaystyle chi _ {n}\uff08z\uff09= z^{n}}} \u306e\u305f\u3081\u306b n \u2208 Z{displaystyle nin {mathbb {z}}} \u3002\u3042\u306a\u305f\u306f\u8b58\u5225\u3057\u307e\u3059 \u03c7n{displaystyle chi _ {n}} n\u3067\u3001\u305d\u3046\u3067\u3059 T^\u2245 Z{displaystyle {hat {mathbb {t}}} cong {mathbb {z}}}}} \u3002 \u30b0\u30eb\u30fc\u30d7 Z{displaystyle {mathbb {z}}} \u30ad\u30e3\u30e9\u30af\u30bf\u30fc\u304c\u3042\u308a\u307e\u3059 \u03c7z\uff1a Z\u2192 T{displaystyle chi _ {z}\uff1a{mathbb {z}} rightarrow {mathbb {t}}} \u3001 \u03c7z\uff08 n \uff09\uff09 = zn{displaystyle chi _ {z}\uff08n\uff09= z^{n}}} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 \u3068 \u2208 T{displaystyle zin {mathbb {t}}} \u3002\u5272\u308a\u5f53\u3066 \u03c7z\u21a6 \u3068 {displaystyle chi _ {z} mapsto z} \u914d\u9054\u3057\u307e\u3059 Z^\u2245 T{displaystyle {hat {mathbb {z}}} cong {mathbb {t}}}}} \u3002 R{displaystyle mathbb {r}} \u30ea\u30f3\u30af\u3068\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30c8\u30dd\u30ed\u30b8\u30fc\u3068\u3057\u3066\u306e\u8ffd\u52a0\u306b\u3088\u308a\u3001\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u304c\u30a2\u30d9\u30eb\u306e\u30b0\u30eb\u30fc\u30d7\u3067\u3059\u3002\u3059\u3079\u3066\u306e\u30ad\u30e3\u30e9\u30af\u30bf\u30fc \u30d0\u30c4 \uff1a R\u2192 T{displaystyle chi\uff1a{mathbb {r}} rightarrow {mathbb {t}}}}} \u5f62\u304c\u3042\u308a\u307e\u3059 \u03c7z\uff08 \u30d0\u30c4 \uff09\uff09 = eixz{displaystyle chi _ {z}\uff08x\uff09= e^{ixz}} \u306e\u305f\u3081\u306b \u3068 \u2208 R{displaystyle zin {mathbb {r}}} \u3002\u3042\u306a\u305f\u306f\u8b58\u5225\u3057\u307e\u3059 \u03c7z{displaystyle chi _ {z}} Z\u3067\u3001\u305d\u3046\u3067\u3059 R^\u2245 R{displaystyle {hat {mathbb {r}}} cong {mathbb {r}}}}} \u6700\u521d\u306f\u91cf\u3068\u3057\u3066\u3002\u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \uff08 \u03c7zde \u03c7w\uff09\uff09 \uff08 \u30d0\u30c4 \uff09\uff09 = \u03c7z+w\uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle\uff08chi _ {z} cdot chi _ {w}\uff09\uff08x\uff09= chi _ {z+w}\uff08x\uff09} \u3059\u3079\u3066\u306e\u305f\u3081\u306b \u30d0\u30c4 \u2208 R{displaystylexin {mathbb {r}}} \u305d\u3057\u3066\u30a4\u30e9\u30b9\u30c8 \u3068 \u21a6 \u03c7z{displaystyle zmapsto chi _ {z}} \u540c\u8cea\u6027\u304c\u3042\u308b\u306e\u3067\u3001\u3042\u306a\u305f\u304c\u6301\u3063\u3066\u3044\u307e\u3059 R\u2245 R^{displaystyle {mathbb {r}} cong {hat {mathbb {r}}}}}} \u307e\u305f\u3001\u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3068\u3057\u3066\u3002 \u30c7\u30ab\u30eb\u30c8\u88fd\u54c1\u3092\u542b\u3080G\u304a\u3088\u3073H\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3067\u3059 g \u00d7 h {displaystyle gtimes h} \u3002\u6b21\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059 \uff08 \u30d0\u30c4 \u3001 \u03c6 \uff09\uff09 \u2208 G^\u00d7 H^{displayStyle\uff08chi\u3001psi\uff09in {hat {g}} times {hat {h}}} \u4e0a\u306e\u30ad\u30e3\u30e9\u30af\u30bf\u30fc g \u00d7 h {displaystyle gtimes h} \u3001 \u3082\u3057\u3082 \uff08 \u30d0\u30c4 \u3001 \u03c6 \uff09\uff09 \uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \u30d0\u30c4 \uff08 \u30d0\u30c4 \uff09\uff09 de \u03c6 \uff08 \u3068 \uff09\uff09 {displaystyle\uff08chi\u3001psi\uff09\uff08x\u3001y\uff09= chi\uff08x\uff09cdot psi\uff08y\uff09} \u30d7\u30c3\u30c8\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u30b0\u30eb\u30fc\u30d7\u30db\u30e2\u30eb\u30d5\u30a3\u30ba\u30e0\u3092\u53d6\u5f97\u3057\u307e\u3059 G\u00d7H^\u2245 G^\u00d7 H^{displayStyle {widehat {gtimes h}} cong {hat {g}} times {hat {h}}} \u3002 \u3057\u305f\u304c\u3063\u3066\u3001\u4ed6\u306b\u3082\u591a\u304f\u306e\u4f8b\u304c\u3042\u308a\u307e\u3059\uff1a \u3042\u306a\u305f\u306f\u81ea\u7136\u306a\u30a4\u30e9\u30b9\u30c8\u3092\u6301\u3063\u3066\u3044\u307e\u3059 \u30d5\u30a1\u30a4 \uff1a g \u2192 G^^\u3001 \uff08 \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \uff09\uff09 \uff09\uff09 \uff08 \u30d0\u30c4 \uff09\uff09 \uff1a= \u30d0\u30c4 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle phi\uff1agrightarrow {hat {g}}}} ,,\uff08phi\uff08x\uff09\uff09\uff08chi\uff09\uff1a= chi\uff08x\uff09} \u3002 Pontrjagin\u6587 \u3053\u306e\u30a4\u30e9\u30b9\u30c8\u306f\u5e38\u306b\u30c8\u30dd\u30ed\u30b8\u30fc\u30b0\u30eb\u30fc\u30d7\u306e\u540c\u578b\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u540d\u524d\u3092\u6b63\u5f53\u5316\u3057\u307e\u3059 \u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7 G\u304b\u3089\u3001\u4e0a\u8a18\u306e\u6587\u306b\u3088\u308b\u3068\u3042\u306a\u305f\u306f\u304b\u3089\u884c\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067 G^{displaystyle {hat {g}}} \u66f4\u65b0\u3055\u308c\u305f\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u30d5\u30a9\u30fc\u30e1\u30fc\u30b7\u30e7\u30f3\u3092\u901a\u3058\u3066\u56de\u5fa9\u3057\u307e\u3059\u3002 Pontrjagin\u306e\u4e8c\u91cd\u6027\u306b\u3088\u308a\u3001\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30a2\u30d9\u30eb\u30b0\u30eb\u30fc\u30d7G\u3068\u305d\u306e\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u3068\u306e\u9593\u306b\u591a\u304f\u306e\u95a2\u4fc2\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059 G^{displaystyle {hat {g}}} \u3002\u4ee3\u6570\u7684\u7279\u6027\u3068\u30c8\u30dd\u30ed\u30b8\u30fc\u7279\u6027\u306e\u9593\u306b\u306f\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002\u6a21\u7bc4\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff1a G\u306f\u63a7\u3048\u3081\u3067\u3059 \u21d4 {displaystyle leftrightarrow}  G^{displaystyle {hat {g}}} \u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002 G\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059 \u21d4 {displaystyle leftrightarrow}  G^{displaystyle {hat {g}}} \u63a7\u3048\u3081\u3067\u3059\u3002 \u6b21\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3068\u540c\u7b49\u3067\u3059\u3002 \u5225\u306e\u63a5\u7d9a\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u3001\u6b21\u306e\u540c\u7b49\u6027\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 \u4e00\u5b9a\u306e\u540c\u6027\u611b \u30d5\u30a1\u30a4 \uff1a g \u2192 h {displaystyle varphi\uff1agrightarrow h} \u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u53b3\u5bc6\u306b \u3001 \u3082\u3057\u3082 \u30d5\u30a1\u30a4 {displaystyle varphi} \u30a4\u30e9\u30b9\u30c8\u3068\u3057\u3066 g \u2192 \u30d5\u30a1\u30a4 \uff08 g \uff09\uff09 {displaystyle grightarrow varphi\uff08g\uff09}  \u958b\u3051\u308b IS\u3001d\u3002 H.\u3059\u3079\u3066\u306e\u30aa\u30fc\u30d7\u30f3\u91cf\u306e\u753b\u50cf\u306f\u3001\u306e\u5199\u771f\u3067\u6bd4\u8f03\u7684\u958b\u3044\u3066\u3044\u307e\u3059 \u30d5\u30a1\u30a4 {displaystyle varphi} \u3002 1\u3064\u306e\u30a8\u30d4\u30bd\u30fc\u30c9 … \u2192 g \u2192 h \u2192 … {displaystyle ldots rightarrow grightarrow hirtirarow ldots} \u540c\u6027\u611b\u306e\u610f\u5473 \u53b3\u5bc6\u306b \u3059\u3079\u3066\u306e\u540c\u6027\u611b\u304c\u53b3\u683c\u3067\u3042\u308b\u3068\u304d\u3002\u6700\u5f8c\u306b\u30011\u3064\u306f1\u306e1\u3064\u306e\u8981\u7d20\u30b0\u30eb\u30fc\u30d7\u3092\u6307\u3057\u3001\u89b3\u5bdf\u3055\u308c\u307e\u3057\u305f 1^\u2245 \u521d\u3081 {displaystyle {hat {1}} cong 1} \u6b21\u306e\u6587\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff1a \u591a\u5206 \u521d\u3081 \u2192 \u306e \u2192 g \u2192 h \u2192 \u521d\u3081 {displaystyle 1 rightarrow urightarrow grightarrow hirtirarow 1} \u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u9593\u306e\u4e00\u5b9a\u306e\u4e00\u5b9a\u306e\u540c\u6027\u611b\u3002\u6b21\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u540c\u7b49\u3067\u3059\u3002 1\u2192U\u2192G\u2192H\u21921{displaystyle 1 rightarrow urightarrow grightarrow hirtirarow 1} \u53b3\u683c\u3067\u6b63\u78ba\u306a\u7d50\u679c\u3067\u3059\u3002 1\u2192H^\u2192G^\u2192U^\u21921{displaystyle1rightArrow {hat {h}} rightArrow {hat {g}} rightArrow {hat {u}} rightArrow 1} \u53b3\u683c\u3067\u6b63\u78ba\u306a\u7d50\u679c\u3067\u3059\u3002 \u3053\u308c\u304b\u3089\u3055\u3089\u306b\u7d50\u8ad6\u304c\u5c0e\u304d\u51fa\u3055\u308c\u307e\u3059\u3002 Pontrjagin\u306e\u4e8c\u91cd\u6027\u306f\u3001\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u306b\u3068\u3063\u3066\u69cb\u9020\u7406\u8ad6\u306e\u91cd\u8981\u306a\u30c4\u30fc\u30eb\u3067\u3059\u3002\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u304c\u547c\u3070\u308c\u307e\u3059 \u30b3\u30f3\u30d1\u30af\u30c8\u306b\u751f\u6210\u3055\u308c\u307e\u3059 G\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b5\u30d6\u30bb\u30c3\u30c8\u304c\u3042\u308b\u5834\u5408\u3001G\u306fG\u3092\u30b0\u30eb\u30fc\u30d7\u3068\u3057\u3066\u751f\u6210\u3057\u307e\u3059\u3002\u63a7\u3048\u3081\u306a\u30b0\u30eb\u30fc\u30d7\u306f\u3001\u6700\u7d42\u7684\u306b\u751f\u6210\u3055\u308c\u308b\u3068\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u4f5c\u6210\u3055\u308c\u307e\u3059\u3002 \u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30a2\u30d9\u30eb\u30b7\u30a7\u30b0\u30eb\u30fc\u30d7\u306e\u5834\u5408\u3001\u540c\u7b49\u3067\u3059\u3002 G\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002 g \u2245 Rm\u00d7 Zn\u00d7 k {displaystyle gcong {mathbb {r}}^{m} times {mathbb {z}}^{n} times k} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 m \u3001 n \u2208 N0{displaystyle M\u3001nin {mathbb {n}} _ {0}} K\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3067\u3059\u3002 G^\u2245 Rm\u00d7 Tn\u00d7 d {displaystyle {hat {g}} cong {mathbb {r}}^{m} times {mathbb {t}}^{n} times d} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 m \u3001 n \u2208 N0{displaystyle M\u3001nin {mathbb {n}} _ {0}} D\u306f\u63a7\u3048\u3081\u306a\u30b0\u30eb\u30fc\u30d7\u3067\u3059\u3002 \u8ffd\u52a0\uff1a\u6570\u5024M\u3068N\u306fG\u306b\u3088\u3063\u3066\u660e\u78ba\u306b\u6c7a\u5b9a\u3055\u308c\u3001K\u306fG\u306e\u6700\u5927\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u30b5\u30d6\u30b0\u30eb\u30fc\u30d7\u3067\u3059\u3002 \u8a18\u4e8b\u306e\u8abf\u548c\u5206\u6790\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\u3001\u30ed\u30fc\u30ab\u30eb\u30b3\u30f3\u30d1\u30af\u30c8\u30a2\u30d9\u30eb\u30b0\u30eb\u30fc\u30d7G\u306e\u30c7\u30e5\u30a2\u30eb\u30b0\u30eb\u30fc\u30d7\u306f\u3001\u6298\u308a\u7573\u307f\u4ee3\u6570\u306e\u30b2\u30eb\u30d5\u30a1\u30f3\u30c9\u5909\u63db\u3067\u767a\u751f\u3057\u307e\u3059\u3002 Pontrjagin\u306e\u4e8c\u91cd\u6027\u3001d\u3002 H.\u4e0a\u8a18\u306e\u5272\u308a\u5f53\u3066 g \u21a6 G^{displaystyle gmapsto {hat {g}}} \u3068 \u30d5\u30a1\u30a4 \u21a6 \u03c6^{displaystyle varphi mapstosto {hat {varphi}}} \u5730\u5143\u306e\u30b3\u30f3\u30d1\u30af\u30c8\u304b\u3089\u30a2\u30d9\u30eb\u306e\u30b0\u30eb\u30fc\u30d7\u3068\u5b89\u5b9a\u3057\u305f\u6e96\u540c\u578b\u306f\u3001\u660e\u3089\u304b\u306b\u77db\u76fe\u3057\u305f\u30e9\u30b8\u30aa\u3067\u3059\u3002\u3053\u306e\u30e9\u30b8\u30aa\u306e2\u56de\u306e\u9023\u7d9a\u306f\u3001\u540c\u4e00\u306e\u30e9\u30b8\u30aa\u306b\u3064\u306a\u304c\u308a\u307e\u3059\uff08\u3088\u308a\u6b63\u78ba\u306b\u306f\uff1a\u540c\u4e00\u306e\u30e9\u30b8\u30aa\u3068\u306e\u81ea\u7136\u306a\u540c\u7b49\u6027\u306b\uff09\u3002 \u30ea\u30f3H.\u30eb\u30fc\u30df\u30b9\uff1a \u62bd\u8c61\u9ad8\u8abf\u6ce2\u89e3\u6790\u306e\u7d39\u4ecb \u3001D\u3002VanNostrand Co\u30011953 \u30a6\u30a9\u30eb\u30bf\u30fc\u30fb\u30eb\u30fc\u30c7\u30a3\u30f3\uff1a \u30b0\u30eb\u30fc\u30d7\u306e\u30d5\u30fc\u30ea\u30a8\u5206\u6790 \u30011962\u5e74 E.\u30d2\u30e5\u30fc\u30a4\u30c3\u30c8\u3001K\u3002\u30ed\u30b9\uff1a \u62bd\u8c61\u9ad8\u8abf\u6ce2\u89e3\u6790I\u3001ii \u3001Springer\uff081963\uff09\u3001\uff081970\uff09\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/20778#breadcrumbitem","name":"Pontrjagin Duality-Wikipedia"}}]}]