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- Vasilii Sergeevich Vladimirov (en)
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- G/g043810 (en)
- G/g043820 (en)
- G/g043830 (en)
- G/g043840 (en)
- G/g130030 (en)
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- Oberguggenberger (en)
- Vladimirov (en)
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- Let and If then (en)
- Suppose is a Radon measure, where let be a neighborhood of the support of and let There exists a family of locally functions on such that for every and
Furthermore, is also equal to a finite sum of derivatives of continuous functions on where each derivative has order (en)
- Each of the canonical maps below are TVS isomorphisms:
Here represents the completion of the injective tensor product and has the topology of uniform convergence on bounded subsets. (en)
- Suppose has finite order and Given any open subset of containing the support of , there is a family of Radon measures in , such that for very and (en)
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- Theorem (en)
- Theorem. (en)
- Fubini's theorem for distributions (en)
- Schwartz kernel theorem (en)
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- The lead, in particular, the first paragraph are unnecessary technical. (en)
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- Assumption: For any compact subset we will henceforth assume that is endowed with the subspace topology it inherits from the Fréchet space (en)
- Definition: Elements of are called ' on and is called the ' on . We will use both and to denote this space. (en)
- 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 (en)
- Definition and notation: , denoted by is the continuous dual space of endowed with the topology of uniform convergence on bounded subsets of More succinctly, the space of distributions on is (en)
- is called the and it may also be denoted by (en)
- The is the finest locally convex topology on making all of the inclusion maps continuous . (en)
- As is common in mathematics literature, the space is henceforth assumed to be endowed with its canonical LF topology . (en)
- By definition, a is defined to be a continuous linear functional on Said differently, a distribution on is an element of the continuous dual space of when is endowed with its canonical LF topology. (en)
- Suppose and is an arbitrary compact subset of Suppose an integer such that and is a multi-index with length For define:
while for define all the functions above to be the constant map. (en)
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- Generalized function (en)
- Generalized function algebras (en)
- Generalized function, derivative of a (en)
- Generalized functions, product of (en)
- Generalized functions, space of (en)
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- Spaces of test functions and distributions (en)
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