[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/1077#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/1077","headline":"Hellinger Toeplitz\u306e\u6587\u7ae0Wikipedia","name":"Hellinger Toeplitz\u306e\u6587\u7ae0Wikipedia","description":"before-content-x4 Hellinger Toeplitz\u6587 \u6a5f\u80fd\u5206\u6790\u304b\u3089\u306e\u6570\u5b66\u7684\u6587\u3067\u3059\u3002\u5f7c\u306f\u6570\u5b66\u8005\u306e\u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30d8\u30ea\u30f3\u30b8\u30e3\u30fc\u3068\u30aa\u30c3\u30c8\u30fc\u30fb\u30c8\u30a5\u30a8\u30d7\u30ea\u30c3\u30c4\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002\u3082\u3068\u3082\u3068\u3001\u6587\u306f\u7121\u9650\u306e\u6570\u306e\u53cc\u7dda\u5f62\u5f62\u72b6\u3067\u7b56\u5b9a\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002 [\u521d\u3081] [2] [3] after-content-x4 \u306a\u308c h {displaystyle h} hilbertraum\u3068 t \uff1a h \u2192 h {displaystyleT\uff1ahightarrow h}","datePublished":"2022-04-27","dateModified":"2022-04-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/75a9edddcca2f782014371f75dca39d7e13a9c1b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/75a9edddcca2f782014371f75dca39d7e13a9c1b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/1077","wordCount":3744,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Hellinger Toeplitz\u6587 \u6a5f\u80fd\u5206\u6790\u304b\u3089\u306e\u6570\u5b66\u7684\u6587\u3067\u3059\u3002\u5f7c\u306f\u6570\u5b66\u8005\u306e\u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30d8\u30ea\u30f3\u30b8\u30e3\u30fc\u3068\u30aa\u30c3\u30c8\u30fc\u30fb\u30c8\u30a5\u30a8\u30d7\u30ea\u30c3\u30c4\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002\u3082\u3068\u3082\u3068\u3001\u6587\u306f\u7121\u9650\u306e\u6570\u306e\u53cc\u7dda\u5f62\u5f62\u72b6\u3067\u7b56\u5b9a\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002 [\u521d\u3081] [2] [3]        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u306a\u308c h {displaystyle h} hilbertraum\u3068 t \uff1a h \u2192 h {displaystyleT\uff1ahightarrow h} \u5bfe\u79f0\u7684\u306a\u7dda\u5f62\u6f14\u7b97\u5b50\u3001\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e\u4eba\u306e\u305f\u3081\u306e\u6f14\u7b97\u5b50        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 \u3001 \u3068 \u2208 h {displaystyle x ,, yin h} \u65b9\u7a0b\u5f0f \u27e8 t \u30d0\u30c4 \u3001 \u3068 \u27e9 = \u27e8 \u30d0\u30c4 \u3001 t \u3068 \u27e9 {displaystyle langle tx\u3001yrangle = langle x\u3001tyrangle} \u6e80\u305f\u3059\u3002\u305d\u308c\u304b\u3089 t {displaystylet} \u5b89\u5b9a\u3057\u305f\u3001d\u3002 H.\u9650\u5b9a\u3002 [4]        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5b8c\u6210\u3057\u305f\u30b0\u30e9\u30d5\u304b\u3089\u306e\u6587\u306b\u3088\u308b\u3068\u3001\u4ee5\u4e0b\u3092\u793a\u3059\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002 [5] \u306f \uff08 \u30d0\u30c4 n\uff09\uff09 n\u2208N{displaystyle\uff08x_ {n}\uff09_ {nin mathbb {n}}}} \u30bc\u30ed\u30b7\u30fc\u30b1\u30f3\u30b9\u3068 t \u30d0\u30c4 n{displaystyletx_ {n}} \u53ce\u675f\u3001\u305d\u3046\u3067\u3059 \u30ea\u30e0 n\u2192\u221et \u30d0\u30c4 n= 0 {displaystyle lim _ {nrightarrow infty} tx_ {n} = 0} \u3002 \u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306e\u5b89\u5b9a\u6027\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408 h {displaystyle h} \u3068\u30bb\u30c3\u30c8 \u3068 \uff1a= \u30ea\u30e0 n\u2192\u221et \u30d0\u30c4 n{displaystyle y\uff1a= lim _ {nrightarrow infty} tx_ {n}} \u3001\u6b21\u306b\u7d9a\u304d\u307e\u3059 \u27e8 \u3068 \u3001 \u3068 \u27e9 = \u27e8 limn\u2192\u221et xn\u3001 \u3068 \u27e9 = limn\u2192\u221e\u27e8 t xn\u3001 \u3068 \u27e9 = limn\u2192\u221e\u27e8 xn\u3001 t \u3068 \u27e9 = \u27e8 limn\u2192\u221exn\u3001 t \u3068 \u27e9 = \u27e8 0 \u3001 t \u3068 \u27e9 = 0 \u3001 {displaystyle langle y\u3001yrangle = langle lim _ {nrightarrow infty} tx_ {n}\u3001yrangle = lim _ _ _ {nrightarrow infty}\u30e9\u30f3\u30b0\u30ebTx_ {n}\u3001yrangle = lim _ _ _ {nightarrow inf} ngle lim _ {nirtirrow inf smang _ x_ \u3001} \u307e\u305f \u3068 = 0 {displaystyle y = 0} \u3002 \u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u4ee5\u6765 t {displaystylet} \u7dda\u5f62\u3067\u5b89\u5b9a\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u5236\u9650\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u3069\u3053\u3067\u3082\u5bfe\u79f0\u7684\u3067\u3059 h {displaystyle h} \u5b9a\u7fa9\u3055\u308c\u305f\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306fself -jam\u3067\u3059\u3002 \u6291\u5236\u3055\u308c\u3066\u3044\u306a\u3044\u81ea\u5df1\u751f\u6210\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306f\u3001\u305b\u3044\u305c\u3044hilbertraum\u306e\u5bc6\u306a\u30b5\u30d6\u30bb\u30c3\u30c8\u3067\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 Hellinger Toeplitz\u306e\u6587\u306e\u72b6\u614b\u3092\u5f31\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a \u306a\u308c h 1{displaystyle h_ {1}} \u3068 h 2{displaystyle h_ {2}} \u30d2\u30eb\u30d0\u30fc\u306e\u5922\u3068 t \uff1a h 1\u2192 h 2{displayStyle T\uff1aH_ {1} rightArrow H_ {2}} \u88dc\u52a9\u8005\u3092\u6301\u3063\u3066\u3044\u308b\u7dda\u5f62\u6f14\u7b97\u5b50\u3001\u3064\u307e\u308a\u3001\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u304c\u3044\u307e\u3059 s \uff1a h 2\u2192 h 1{displaystyle s\uff1ah_ {2} rightArrow H_ {1}} \u307f\u3093\u306a\u306e\u305f\u3081\u306e\u3082\u306e \u30d0\u30c4 \u2208 h 1{displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059{1}} \u3068 \u3068 \u2208 h 2{displaystyle yin h_ {2}} \u65b9\u7a0b\u5f0f \u27e8 t \u30d0\u30c4 \u3001 \u3068 \u27e9H2= \u27e8 \u30d0\u30c4 \u3001 s \u3068 \u27e9H1{displaystyle langle tx\u3001yrangle _ {h_ {2}} = langle x\u3001syrangle _ {h_ {1}}} \u6e80\u305f\u3059\u3002\u3088\u308a\u3082 t {displaystylet} \u3068 s {displaystyleS} \u5b89\u5b9a\u3002 \u8a3c\u660e\u306f\u985e\u4f3c\u3057\u3066\u3044\u307e\u3059\u3002 \u6a5f\u80fd\u5206\u6790\u306e\u500b\u3005\u306e\u53c2\u7167\u307e\u305f\u306f\u5c02\u9580\u5bb6\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u2191  R. E.\u30a8\u30c9\u30ef\u30fc\u30c9\uff1a Hellingertoeplitz\u5b9a\u7406 \u3002\u306e\uff1a \u30ed\u30f3\u30c9\u30f3\u6570\u5b66\u5354\u4f1a\u306e\u30b8\u30e3\u30fc\u30ca\u30eb \u3002 S1-32\u3001 \u3044\u3044\u3048\u3002  4 \u30011957\u5e7410\u6708\u3001 S.  499\u2013501 \u3001doi\uff1a 10.1112 \/ jlms \/ s1-32.4.499 \uff08\u82f1\u8a9e\u3001 wiley.com [2022\u5e7411\u670810\u65e5\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30d8\u30ea\u30f3\u30b8\u30e3\u30fc\u3001\u30aa\u30c3\u30c8\u30fc\u30fb\u30c8\u30a5\u30a8\u30d7\u30ea\u30c3\u30c4\uff1a \u7121\u9650\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u7406\u8ad6\u306e\u57fa\u790e \u3002\u306e\uff1a \u6570\u5b66\u7684\u306a\u5e74\u6b21 \u3002 \u30d0\u30f3\u30c9  69 \u3001 \u3044\u3044\u3048\u3002  3 \u30011910\u5e749\u6708\u3001ISSN 0025-5831 \u3001 S.  321  ff \u3002\u3001doi\uff1a 10.1007\/BF01456325 \uff08 springer.com [2022\u5e7411\u670810\u65e5\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30a8\u30eb\u30f3\u30b9\u30c8\u30fb\u30d8\u30ea\u30f3\u30b8\u30e3\u30fc\u3001\u30aa\u30c3\u30c8\u30fc\u30fb\u30c8\u30a5\u30a8\u30d7\u30ea\u30c3\u30c4\uff1a \u7121\u9650\u306e\u591a\u304f\u306e\u672a\u77e5\u306e\u7a4d\u5206\u65b9\u7a0b\u5f0f\u3068\u65b9\u7a0b\u5f0f \u3002 Vieweg+Teubner Verlag\u3001Wiesbaden 1928\u3001ISBN 978-3-663-15348-1\u3001doi\uff1a 10,1007\/978-3-663-15917-9 \uff08 springer.com [2022\u5e7411\u670810\u65e5\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30de\u30fc\u30b7\u30e3\u30eb\u30fb\u30cf\u30fc\u30d9\u30a4\u30fb\u30b9\u30c8\u30fc\u30f3\uff1a \u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u306e\u7dda\u5f62\u5909\u63db\u3068\u5206\u6790\u3078\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3 \u3002\u30a2\u30e1\u30ea\u30ab\u6570\u5b66\u5354\u4f1a\u3001\u30cb\u30e5\u30fc\u30e8\u30fc\u30af1932\u3001ISBN 0-8218-1015-4\u3001 S.  59  ff \u3002 \uff08\u82f1\u8a9e\u3001 archive.org [2022\u5e7411\u670810\u65e5\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30c0\u30fc\u30af\u30fb\u30a6\u30a7\u30eb\u30ca\u30fc\uff1a \u6a5f\u80fd\u7684\u89e3\u6790 \uff08= \u30b9\u30d7\u30ea\u30f3\u30ac\u30fc\u6559\u79d1\u66f8 \uff09\u3002 Springer Berlin Heidelberg\u3001Berlin\u3001Heidelberg 2018\u3001ISBN 978-3-662-55406-7\u3001 S.  260  ff \u3002\u3001doi\uff1a 10,1007\/978-3-662-55407-4 \uff08 springer.com [2022\u5e7411\u670810\u65e5\u30a2\u30af\u30bb\u30b9]\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\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/1077#breadcrumbitem","name":"Hellinger Toeplitz\u306e\u6587\u7ae0Wikipedia"}}]}]