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and possible to do so, then terminology that a reader is unlikely to be familiar with should be briefly defined/described within this article, instead of just having a link to the article about the term (this is because ideally, a "typical" reader should not have to go down a rabbit hole of
Knowledge links and search through various articles in order to understand something stated in
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689:"a 'typical' reader should not have to go down a rabbit hole of wikipedia links" to understand an article, but I would say that this article is (at least somewhat) an exception to this rule, because it requires a much higher than average amount of prerequisite knowledge (again, please correct me if I am wrong)
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I think the recent changes are absolutely in the right direction. I made a few minor edits, mostly to remove "scare" quotes about the difficulties of defining the topology on the space of distributions (it's enough to refer to the relevant article). Also, I think more of the discussion on topologies
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My comment about technicality and style of the article does not mean I endorse the accuracy of every claim in the April version I refer to. If there are incorrect statements, they can be corrected without resorting to the drastic changes you have made to the article. By all means, fix errors. But
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I recently learned distributions and I found it frustrating the first time I glanced at this article, hoping for an overview of the subject. This issue was not even technicality: I understand Fréchet spaces and topological linear spaces. The article was just not reader-friendly and felt more like a
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be described using sequences (let along a metric). Suggestions about how to define and describe these topologies to readers who are not used to dealing with non-sequential (and also non-metrizable) spaces would be welcome. The current description of these topologies is (unfortunately) technical and
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Is it safe to assume that the reader has studied Fréchet spaces? My guess is probably not and so the reader should not be assumed to know about Fréchet space. But if they are familiar with the basics of Banach spaces then the required knowledge for Fréchet spaces can be described using Banach space
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I think that it is safe to assume that the reader has knowledge of calculus. But before we start editing this article to make it less technical, it's important to know what else we can assume about a "typical" reader of this article. This is important because, for example, whenever it is reasonable
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I believe distributions are common in physics (please correct me if I'm wrong), and I am not sure that physics students will know about
Frechet spaces (I am not a physics student myself, so I don't even know if physics undergrads learn any topology) – so perhaps the ultimate goal is to make this
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The April 2020 version opens with a Basic Idea section that illustrates the essence of the subject. The Sep 2020 version introduces a lot of notation and ancillary concepts, much of which does not seem necessary to introduce the definition of a test function.
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I am in favor of creating a separate article for the canonical LF topology (this topology has been studied enough to warrant its own article) and in this way we can simplify the article on distributions by placing some technical details into this new article.
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1576:"Tempered distributions" is used but not defined in this article. I've heard they are "distributions that are upper bounded by polynomials", which I'm not quite sure how to make precise. I've also heard the more
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Distributions are unfortunately an innately technical topic. However, I am fine with simplifying the article but not at the expense of adding false-but-simple information or removing important information.
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Over time, I will try to make this article less technical. However, we first need to establish what assumptions can and can not be made about this article and its "typical" reader. According to
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The series of edits made by the same user since May 2020 has made this article overly technical, and no longer in the spirit of a
Knowledge article on the subject. To see thepoint, compare the
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Also, the old article was missing important information such as how to extend differential operators to distributions, which is arguably is one of the more important uses of distributions.
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Is it safe to assume that the reader has studied Banach spaces? (If not, then the Fréchet spaces and related notions that are used in this article will need more detailed explanations).
586:"consider the typical level where the topic is studied (for example, secondary, undergraduate, or postgraduate) and write the article for readers who are at the previous level." Also,
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I would strongly urge that the article be edited back to resemble the April 2020 version, and any advanced material being added after the the simplified introduction to the subject.
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test functions are the fundamental ones for distributions. As a minor point, I'd denote the regular distribution associated with multiplication by a locally integrable function
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appear in this article. The correct definition of the canonical LF-topology on the space of test functions is unfortunately technical.
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Is it safe to assume that the reader has knowledge of general topology (in particular, of non-metrizable topological spaces)?
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define the topology using sequences and this is a non-trivial fact that has been proven. The above false statement should
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As far as the continuity of distributions is concerned, all one needs to say in this article is that a linear functional
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The article that you linked to contained false information such as the last sentence of this claim: " The elements of D(
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No one looking for a straightforward explanation of distributions will be able to get through the current article.
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in terms of (the extension of?) linear functions on
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Is it safe to assume that the reader is likely an advanced undergraduate or higher? (I personally think so).
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1276:{\displaystyle |T(\varphi )|\leq C\sum _{|\alpha |\leq n}\|\partial ^{\alpha }\varphi \|_{\infty }}
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article accessible to physicists? It would be helpful if others could give their thoughts on this.
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on
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Is it safe to assume that the reader has studied metric spaces? (I personally think that it is).
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this does not justify the excessively technical approach you have followed in your rewrite.
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However, these changes would require a lot of rewriting of the first part of this article.
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I'd like for it to be less technical but I'm not sure how to make it less technical.
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Completely agree about moving discussion of TVS topologies to another article
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Is it safe to assume that the reader is likely a graduate student or higher?
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with the last version prior to the series of edits by the same editor, the
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For instance, we can make the presentation less general by replacing
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can be moved elsewhere, and all (or nearly all?) of the material on
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and the sequence and all of its derivatives converge uniformly on
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Is it safe to assume that the reader has studied non-metrizable
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KINDLY DO NOT ERASE OTHER PEOPLE'S POSTS WHEN YOU POST YOUR OWN
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