Talk:Distribution (mathematics): Difference between revisions

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imported>Aleksander Stos
imported>Aleksander Stos
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|                abc = Distribution
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|                  by = --[[User:Paul Wormer|Paul Wormer]] 07:53, 12 November 2007 (CST)
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== Multi-index ==
== Multi-index ==


When I set up this article as a stub, I was thinking of φ as a function of ''one'' (real) variable. The use of the multi-index α suggests a generalization to functions of more than one variable. However, nowhere in the article this generalization is stated explicitly.--[[User:Paul Wormer|Paul Wormer]] 07:27, 8 December 2007 (CST)
When I set up this article as a stub, I was thinking of φ as a function of ''one'' (real) variable. The use of the multi-index α suggests a generalization to functions of more than one variable. However, nowhere in the article this generalization is stated explicitly.--[[User:Paul Wormer|Paul Wormer]] 07:27, 8 December 2007 (CST)
:I'd prefer an article in <math>R^n</math>, as it's the most natural setting in analysis. The reason is that we have fundamental theorems (called Sobolev Lemma(s)) for regularity of distributions and there  the dimension is the crucial parameter. But I agree that a basic article ''can'' be written in one dimension. So, perhaps, for simplicity of presentation it should (a section with quite simple generalisation can be added later). I'll handle (temporarily delete) the formulas with multi-index. Others may have different views.[[User:Aleksander Stos|Aleksander Stos]] 09:56, 8 December 2007 (CST)
:I'd prefer an article in <math>R^n</math>, as it's the most natural setting in analysis. The reason is that we have fundamental theorems (called Sobolev Lemma(s)) for regularity of distributions and there  the dimension is the crucial parameter. But I agree that a basic article ''can'' be written in one dimension. So, perhaps, for simplicity of presentation it should (a section with quite simple generalisation can be added later). I'll handle (temporarily delete) the formulas with multi-index. Others may have different views.[[User:Aleksander Stos|Aleksander Stos]] 09:56, 8 December 2007 (CST)

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 Definition:  Objects which generalize functions, used to formulate generalized solutions of partial differential equations. [d] [e]
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Multi-index

When I set up this article as a stub, I was thinking of φ as a function of one (real) variable. The use of the multi-index α suggests a generalization to functions of more than one variable. However, nowhere in the article this generalization is stated explicitly.--Paul Wormer 07:27, 8 December 2007 (CST)

I'd prefer an article in , as it's the most natural setting in analysis. The reason is that we have fundamental theorems (called Sobolev Lemma(s)) for regularity of distributions and there the dimension is the crucial parameter. But I agree that a basic article can be written in one dimension. So, perhaps, for simplicity of presentation it should (a section with quite simple generalisation can be added later). I'll handle (temporarily delete) the formulas with multi-index. Others may have different views.Aleksander Stos 09:56, 8 December 2007 (CST)
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