. "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u0430 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0424\u0443\u0440'\u0454 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u0431\u0430\u0433\u0430\u0442\u043E \u0442\u0438\u043F\u0456\u0432 \u0444\u0443\u043D\u043A\u0446\u0456\u0439 \u043C\u043E\u0436\u043B\u0438\u0432\u043E \u0432\u0456\u0434\u043D\u043E\u0432\u0438\u0442\u0438, \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u044E\u0447\u0438 \u0457\u0445 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454.\u0406\u043D\u0442\u0443\u0457\u0442\u0438\u0432\u043D\u043E \u0446\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u043C\u043E\u0436\u043D\u0430 \u0437\u0440\u043E\u0437\u0443\u043C\u0456\u0442\u0438 \u0442\u0430\u043A: \u044F\u043A\u0449\u043E \u0432\u0456\u0434\u043E\u043C\u0430 \u0447\u0430\u0441\u0442\u043E\u0442\u0430 \u0442\u0430 \u0444\u0430\u0437\u0430 \u043A\u043E\u043B\u0438\u0432\u0430\u043D\u044C \u0445\u0432\u0438\u043B\u0456, \u0442\u043E \u043C\u043E\u0436\u043B\u0438\u0432\u043E \u0432\u0456\u0434\u043D\u043E\u0432\u0438\u0442\u0438 \u043F\u043E\u0447\u0430\u0442\u043A\u043E\u0432\u0438\u0439 \u0441\u0442\u0430\u043D \u0446\u0456\u0454\u0457 \u0445\u0432\u0438\u043B\u0456. \u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u044F\u043A\u0449\u043E \u0444\u0443\u043D\u043A\u0446\u0456\u044F \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u043F\u0435\u0432\u043D\u0456 \u0443\u043C\u043E\u0432\u0438, \u0442\u043E \u0437 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454, \u0449\u043E I\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u041E\u0441\u0442\u0430\u043D\u043D\u044E \u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u044C\u043D\u043E\u044E \u0442\u0435\u043E\u0440\u0435\u043C\u043E\u044E \u0424\u0443\u0440'\u0454. \u0406\u043D\u0448\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u043D\u043D\u044F \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0443 \u0442\u043E\u043C\u0443, \u0449\u043E \u044F\u043A\u0449\u043E \u2014 \u0444\u043B\u0456\u043F-\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440, \u0442\u043E\u0431\u0442\u043E , \u0442\u043E"@uk . . "In matematica, il teorema di inversione di Fourier, definisce le condizioni di esistenza per l'inversa della trasformata di Fourier, detta anche antitrasformata di Fourier, la quale permette di risalire ad una funzione conoscendo la sua trasformata attraverso la formula di inversione di Fourier. Una versione alternativa del teorema \u00E8 il teorema di inversione di Mellin, che pu\u00F2 essere applicato anche alla trasformata di Fourier grazie alla semplice relazione che le lega."@it . . . . "Na matem\u00E1tica, o teorema inverso de Fourier diz que, para muitos tipos de fun\u00E7\u00F5es, \u00E9 poss\u00EDvel recuperar uma fun\u00E7\u00E3o a partir de sua transformada de Fourier. Intuitivamente, pode ser visto como a prova de que se sabemos frequ\u00EAncia e fase de uma onda, podemos reconstruir sua onda original com precis\u00E3o. O teorema diz que se temos uma fun\u00E7\u00E3o satisfazendo certas condi\u00E7\u00F5es, e usarmos a conven\u00E7\u00E3o para a transformada de Fourier de que Em outras palavras, o teorema diz que Esta \u00FAltima equa\u00E7\u00E3o \u00E9 chamado o teorema integral de Fourier. Outra forma de enunciar o teorema \u00E9 notar que, se R \u00E9 o operador de giro i.e. Rf(x):=f(\u2212x), ent\u00E3o O teorema \u00E9 v\u00E1lido quando ambos f e a sua transformada de Fourier, s\u00E3o absolutamente integr\u00E1veis (no sentido de Lebesgue) e f \u00E9 cont\u00EDnua no ponto x. No entanto, mesmo sob condi\u00E7\u00F5es mais gen\u00E9ricas do teorema da inversa de Fourier ele ainda funciona. Nestes casos, as integrais acima talvez n\u00E3o fa\u00E7am sentido, ou o teorema pode manter por quase todos os x , ao inv\u00E9s do que para todos os x."@pt . "Th\u00E9or\u00E8me d'inversion de Fourier"@fr . . . . "Na matem\u00E1tica, o teorema inverso de Fourier diz que, para muitos tipos de fun\u00E7\u00F5es, \u00E9 poss\u00EDvel recuperar uma fun\u00E7\u00E3o a partir de sua transformada de Fourier. Intuitivamente, pode ser visto como a prova de que se sabemos frequ\u00EAncia e fase de uma onda, podemos reconstruir sua onda original com precis\u00E3o. O teorema diz que se temos uma fun\u00E7\u00E3o satisfazendo certas condi\u00E7\u00F5es, e usarmos a conven\u00E7\u00E3o para a transformada de Fourier de que Em outras palavras, o teorema diz que Esta \u00FAltima equa\u00E7\u00E3o \u00E9 chamado o teorema integral de Fourier."@pt . "En matem\u00E1ticas, el teorema de la inversi\u00F3n de Fourier dice que para muchos tipos de funciones es posible recuperar una funci\u00F3n a partir de su transformada de Fourier. Intuitivamente, puede verse como la afirmaci\u00F3n de que si se conoce toda la informaci\u00F3n relativa a la frecuencia y la fase de una onda, entonces se puede reconstruir con precisi\u00F3n la onda original.\u200B El teorema dice que si se tiene una funci\u00F3n que satisface ciertas condiciones, y se usa la convenci\u00F3n de la transformada de Fourier seg\u00FAn la que entonces En otras palabras, el teorema dice que"@es . "Teorema di inversione di Fourier"@it . . . . . . . . . . . . "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u0430 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0424\u0443\u0440'\u0454 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u0431\u0430\u0433\u0430\u0442\u043E \u0442\u0438\u043F\u0456\u0432 \u0444\u0443\u043D\u043A\u0446\u0456\u0439 \u043C\u043E\u0436\u043B\u0438\u0432\u043E \u0432\u0456\u0434\u043D\u043E\u0432\u0438\u0442\u0438, \u0432\u0438\u043A\u043E\u0440\u0438\u0441\u0442\u043E\u0432\u0443\u044E\u0447\u0438 \u0457\u0445 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454.\u0406\u043D\u0442\u0443\u0457\u0442\u0438\u0432\u043D\u043E \u0446\u0435 \u0442\u0432\u0435\u0440\u0434\u0436\u0435\u043D\u043D\u044F \u043C\u043E\u0436\u043D\u0430 \u0437\u0440\u043E\u0437\u0443\u043C\u0456\u0442\u0438 \u0442\u0430\u043A: \u044F\u043A\u0449\u043E \u0432\u0456\u0434\u043E\u043C\u0430 \u0447\u0430\u0441\u0442\u043E\u0442\u0430 \u0442\u0430 \u0444\u0430\u0437\u0430 \u043A\u043E\u043B\u0438\u0432\u0430\u043D\u044C \u0445\u0432\u0438\u043B\u0456, \u0442\u043E \u043C\u043E\u0436\u043B\u0438\u0432\u043E \u0432\u0456\u0434\u043D\u043E\u0432\u0438\u0442\u0438 \u043F\u043E\u0447\u0430\u0442\u043A\u043E\u0432\u0438\u0439 \u0441\u0442\u0430\u043D \u0446\u0456\u0454\u0457 \u0445\u0432\u0438\u043B\u0456. \u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u044F\u043A\u0449\u043E \u0444\u0443\u043D\u043A\u0446\u0456\u044F \u0437\u0430\u0434\u043E\u0432\u043E\u043B\u044C\u043D\u044F\u0454 \u043F\u0435\u0432\u043D\u0456 \u0443\u043C\u043E\u0432\u0438, \u0442\u043E \u0437 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u043D\u044F \u0424\u0443\u0440'\u0454 \u0444\u0443\u043D\u043A\u0446\u0456\u0457 \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454, \u0449\u043E I\u043D\u0448\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u041E\u0441\u0442\u0430\u043D\u043D\u044E \u0440\u0456\u0432\u043D\u0456\u0441\u0442\u044C \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u044C\u043D\u043E\u044E \u0442\u0435\u043E\u0440\u0435\u043C\u043E\u044E \u0424\u0443\u0440'\u0454. \u0406\u043D\u0448\u0435 \u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u043D\u043D\u044F \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0443 \u0442\u043E\u043C\u0443, \u0449\u043E \u044F\u043A\u0449\u043E \u2014 \u0444\u043B\u0456\u043F-\u043E\u043F\u0435\u0440\u0430\u0442\u043E\u0440, \u0442\u043E\u0431\u0442\u043E , \u0442\u043E \u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0432\u0438\u043A\u043E\u043D\u0443\u0454\u0442\u044C\u0441\u044F \u0434\u043B\u044F \u0442\u0438\u0445 \u0444\u0443\u043D\u043A\u0446\u0456\u0439 \u0442\u0430 \u0457\u0445 \u043F\u0435\u0440\u0435\u0442\u0432\u043E\u0440\u0435\u043D\u044C \u0424\u0443\u0440'\u0454, \u044F\u043A\u0456 \u0454 (\u0437\u0430 \u041B\u0435\u0431\u0435\u0433\u043E\u043C), \u0456 \u0444\u0443\u043D\u043A\u0446\u0456\u0439 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0438\u0445 \u0443 \u0442\u043E\u0447\u0446\u0456 .\u041E\u0434\u043D\u0430\u043A, \u043D\u0430\u0432\u0456\u0442\u044C \u0437\u0430 \u0431\u0456\u043B\u044C\u0448 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u0445 \u0443\u043C\u043E\u0432 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u0430 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0424\u0443\u0440'\u0454 \u043C\u0430\u0454 \u043C\u0456\u0441\u0446\u0435.\u0423 \u0446\u0438\u0445 \u0432\u0438\u043F\u0430\u0434\u043A\u0430\u0445 \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B\u0438, \u0432\u043A\u0430\u0437\u0430\u043D\u0456 \u0432\u0438\u0449\u0435, \u043C\u043E\u0436\u0443\u0442\u044C \u043D\u0435 \u0437\u0431\u0456\u0433\u0430\u0442\u0438\u0441\u044F \u0443 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u043E\u043C\u0443 \u0441\u0435\u043D\u0441\u0456."@uk . . . . . . "En matem\u00E1ticas, el teorema de la inversi\u00F3n de Fourier dice que para muchos tipos de funciones es posible recuperar una funci\u00F3n a partir de su transformada de Fourier. Intuitivamente, puede verse como la afirmaci\u00F3n de que si se conoce toda la informaci\u00F3n relativa a la frecuencia y la fase de una onda, entonces se puede reconstruir con precisi\u00F3n la onda original.\u200B El teorema dice que si se tiene una funci\u00F3n que satisface ciertas condiciones, y se usa la convenci\u00F3n de la transformada de Fourier seg\u00FAn la que entonces En otras palabras, el teorema dice que Esta \u00FAltima ecuaci\u00F3n se denomina teorema integral de Fourier. Otra forma de establecer el teorema es observar que si es el operador de volcado, es decir, , entonces El teorema se cumple si tanto como su transformada de Fourier son absolutamente integrables (en el sentido de la integral de Lebesgue) y es continua en el punto . Sin embargo, incluso en condiciones m\u00E1s generales, se dispone de versiones del teorema de la inversi\u00F3n de Fourier. En estos casos, las integrales anteriores pueden no tener sentido, o el teorema puede ser v\u00E1lido para casi todos los en lugar de para todo .\u200B"@es . . . "Fourier inversion theorem"@en . "Teorema da transformada inversa de Fourier"@pt . . . . . . "In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely. The theorem says that if we have a function satisfying certain conditions, and we use the convention for the Fourier transform that then In other words, the theorem says that This last equation is called the Fourier integral theorem."@en . "382445"^^ . . . . . . . . . . . . . . . . . . "Teorema de la inversi\u00F3n de Fourier"@es . "\u041E\u0431\u0435\u0440\u043D\u0435\u043D\u0430 \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0424\u0443\u0440'\u0454"@uk . . "In matematica, il teorema di inversione di Fourier, definisce le condizioni di esistenza per l'inversa della trasformata di Fourier, detta anche antitrasformata di Fourier, la quale permette di risalire ad una funzione conoscendo la sua trasformata attraverso la formula di inversione di Fourier. Una versione alternativa del teorema \u00E8 il teorema di inversione di Mellin, che pu\u00F2 essere applicato anche alla trasformata di Fourier grazie alla semplice relazione che le lega."@it . . "1101683208"^^ . . . . . "18217"^^ . "En math\u00E9matiques, le th\u00E9or\u00E8me d'inversion de Fourier dit que pour de nombreux types de fonctions, il est possible de retrouver une fonction \u00E0 partir de sa transform\u00E9e de Fourier. En traitement du signal, on pourrait dire que la connaissance de toutes les informations d'amplitude et de phase des ondes constituant un signal permet pr\u00E9cis\u00E9ment de reconstruire ce signal. Le th\u00E9or\u00E8me dit que si nous avons une fonction satisfaisant certaines conditions, on peut d\u00E9finir la transform\u00E9e de Fourier comme et la reconstruction de f \u00E0 partir de sa transform\u00E9e En d'autres termes, le th\u00E9or\u00E8me d'inversion de Fourier dit que Une autre fa\u00E7on d'\u00E9noncer le th\u00E9or\u00E8me est que si est l'op\u00E9rateur d\u00E9fini par , alors Le th\u00E9or\u00E8me est v\u00E9rifi\u00E9 si la fonction f et sa transform\u00E9e de Fourier sont absolument int\u00E9grables (au sens de Lebesgue) et si f est continue au point x. Cependant, m\u00EAme dans des conditions plus g\u00E9n\u00E9rales, les versions du th\u00E9or\u00E8me d'inversion de Fourier restent valables. Dans ces cas, les int\u00E9grales ci-dessus peuvent ne pas converger dans un sens ordinaire."@fr . "En math\u00E9matiques, le th\u00E9or\u00E8me d'inversion de Fourier dit que pour de nombreux types de fonctions, il est possible de retrouver une fonction \u00E0 partir de sa transform\u00E9e de Fourier. En traitement du signal, on pourrait dire que la connaissance de toutes les informations d'amplitude et de phase des ondes constituant un signal permet pr\u00E9cis\u00E9ment de reconstruire ce signal. Le th\u00E9or\u00E8me dit que si nous avons une fonction satisfaisant certaines conditions, on peut d\u00E9finir la transform\u00E9e de Fourier comme et la reconstruction de f \u00E0 partir de sa transform\u00E9e"@fr . "In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely. The theorem says that if we have a function satisfying certain conditions, and we use the convention for the Fourier transform that then In other words, the theorem says that This last equation is called the Fourier integral theorem. Another way to state the theorem is that if is the flip operator i.e. , then The theorem holds if both and its Fourier transform are absolutely integrable (in the Lebesgue sense) and is continuous at the point . However, even under more general conditions versions of the Fourier inversion theorem hold. In these cases the integrals above may not converge in an ordinary sense."@en . . . . . .