Teoría de distribuciones
math statement: The union of all open subsets of in which a distribution vanishes is an open subset of in which vanishes.
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description: mathematischer Begriff @de
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text: The vector space is endowed with the locally convex topology induced by any one of the four families of seminorms described above. This topology is also equal to the vector topology induced by of the seminorms in
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name: Theorem
description: دالة رياضية @ar
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description: kontinua funkcionalo sur spaco de testfunkcioj, kiu ĝeneraligas la koncepton de loke integrebla funkcio @eo
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description: un funcional lineal sobre el espacio de funciones infinitamente diferenciables y compactamente soportadas @es
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first: V.S.
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description: פונקציונל רציף על מרחב של פונקציות מבחן (מרחב שוורץ), שמכליל את מושג הפונקציות האינטגרביליות באופן מקומי @iw
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math statement: Suppose is a distribution on with compact support . There exists a continuous function defined on and a multi-index such that where the derivatives are understood in the sense of distributions. That is, for all test functions on ,
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math statement: Let be a distribution on . There exists a sequence in such that each has compact support and every compact subset intersects the support of only finitely many and the sequence of partial sums defined by converges in to ; in other words we have: Recall that a sequence converges in if and only if it converges pointwise.
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title: Generalized functions, space of
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name: Theorem.
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description: неперервний функціонал на просторі пробних функцій (простір Шварца), що узагальнює поняття локально інтегровних функцій @uk
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author link: Sergei Lvovich Sobolev
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