339:"The infinite sum ... is the Fourier series for ƒ on the interval ." The sentence is not right, how can a sum is a series. Again, "If a function is square-integrable on the interval , then the Fourier series converges to the function at almost every point." Again, the sentence is not right since if the series is just a sum, then how can we talk about convergence? It should be the version I did:
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It is nice having a fellow analyst around. In my brief time here I have had to correct many outrageous claims, ones that were defended vigorously by some editors. I am gald that I have had to "swallow crow" a few times when I realized your being much more careful than I. I wanted to give you my
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Let me, as a much older (I presume) person than you, give you a piece of advice: On one hand, don't believe that math. professors (or even mathematicians) necessary are right and know the truth (I am sure you can follow this part); on the other hand, don't think that others are necessarily
254:
Hey, I left a comment for you on the talk page. I am glad you looked at the article. If you look at the before and after of the edit I point to you'll see I tried hard to improve the article. I was away when you originally left it and did not notice it there until now.
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To me, it seems that it is unbelievable that you are a math professor for the reason that you prefer the previous version, rather than the version I proposed. I am sorry. Looking forward to see your response. (Please just leave it in your talk page!)
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As my personal opinion, I would say my version is pretty accurate, and much better than the previous one, and I don't believe it is useless. Would you please refine the article a little bit? I am looking forward to see it. with best regards.
342:"The sum FN=... forms the Fourier series {FN} for ƒ on the interval ." "If a function f is square-integrable on the interval , then the Fourier series {FN} converges to the function f at almost every point in the interval as N-: -->
1992:. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
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page. You may want to add to this post. I know that a reasonable person (hence, not me) cares about this article, but this time of the year is not only devoted to math... Be a little patient.
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This has happened before, and its a server issue. One of the texvc servers might be down, or one of the caches might have crashed. Usually the problem only lasts a couple of hours.
642:". Maybe I will say something like this in the article. At any rate, I didn't like how the article immediately jumped from concrete examples of complete metric spaces (like
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of the series. It would be possible to rewrite the section in the direction you suggest (but not quite in your way), but most math-editors would, I believe, find it useless.
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Concerning the real matter of your question: there are abuse of language that are common in math articles. You seem to refer to a narrow acception of the word
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Ok. Now I have adjusted the statement from sources. Of course, the case that was in the article now follows easily from the critical case.
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page to explain your changes. There was no clear reason to prefer your version rather than the one that was there for some time already.
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personal, and enthusiastic, welcome to
Knowledge. And should I find myself in France, I will not forget about that drink I owe you.
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2013:
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207:. (and I apologize for any outrageous claims I might have made -- its so much easier to make these, than to be right.)
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describes the
Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to
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if you have any questions or further concerns. Some of the mathematicians here generally lurk in a neighborhood of
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487:. Thanks for spotting the obvious mistake. I don't know why I had accepted the previous edit at face value.
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
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again to fix it. If I misunderstood what happened, or if you have any questions, you can leave a message on
17:
783:"s. If I misunderstood what happened, or if you have any questions, you can leave my operator a message on
1788:\infty \quad \text{implies that} \quad \sum_{n=1}^{\infty} v_n\ \ \text{converges in} \ \ X.</math: -->
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Yes, I should have been clearer. My intention was that a natural thing to use is the family of seminorms
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Finally, be sure that I am not angry when people don't take me seriously. My students do it all the time.
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1, \ldots, \varepsilon_k, 1} - x_{\varepsilon_1, \ldots, \varepsilon_k, -1}\| \ge t, \quad 1 \le k
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left( \int_0^\infty \bigl( t^{-\theta} J(v(t), t; X_0, X_1) \bigr)^q \, {dt \over t} \right)^{1/q}
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Dear
Jackzhp, I am not the author of this sentence "The infinite sum ...", I just want to say that
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Schatten class]] on a
Hilbert space ''H'' are uniformly convex, hence reflexive, when {{nowrap|1
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107:. I hope you like the place and decide to stay. Here are some pages that you might find helpful:
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Here are the main general results about Banach spaces that go back to the time of Banach's book
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1, \ldots, \varepsilon_k, 1} + x_{\varepsilon_1, \ldots, \varepsilon_k, -1}} {2}, \quad 1 \le k
1311:\int_0^\infty \bigl( t^{-\theta} K(u, t; X_0, X_1) \bigr)^q \, {dt \over t} \right)^{1/q}, \ 0
1144:\int_0^\infty \bigl( t^{-\theta} K(u, t; X_0, X_1) \bigr)^q \, {dt \over t} \right)^{1/q}, \ 0
823:"s. If I misunderstood what happened, or if you have any questions, you can leave a message on
153:(~~~~); this will automatically insert your username and the date. If you need help, check out
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interpolation pair (''X'', ''Y'') is said to be of '''exponent''' θ (with {{nowrap|0
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s_{n, k}(t) = 2^{1 + n/2} \int_0^t \psi_{n, k}(u) \, d u, \quad t \in , \ 0 \le k
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M_{\sigma,\varepsilon} \,\, , \left\|\sum\limits_{i=1}^N a_{\sigma(i)}-A \right\|
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P.S. Here is a standard navigation and welcome template, in case you need it:
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Schauder basis#Examples|trigonometric system]] is a basis in ''L''<sup: -->
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2. The theorem is no longer true when the distance is equal to 2.<ref: -->
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complex-valued function is said to '''converge absolutely''' if <math: -->
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series and define such a series to be absolutely convergent if <math: -->
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157:, ask me on my talk page, or ask your question on this page and then place
38:;-). Thanks for pointing out the error. I have corrected the statement.
1913:'I'' is a closed and bounded interval and ''p'', ''q'' are ]s with 1
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I didn't change the text of the article, but I posted a message on the
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Bessaga, Czesław; Pełczyński, Aleksander (1960), "Spaces of continuous
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principle states that if for all ''x'' in ''X'' we have <math: -->
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Dear
Jackzhp, I you want to make changes to a stable article like
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Welcome to
Knowledge. Please don't hesitate to post a message on
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is the panel of editors responsible for conducting the
Knowledge
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872:#Terminology|right-open interval]] {{nowrap| ''I''<sub: -->
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1352:(X_0, X_1)_{\theta, q} = (X_1, X_0)_{1 - \theta, q}, \quad 0
1204:(X_0, X_1)_{\theta, q} = (X_1, X_0)_{1 - \theta, q}, \quad 0
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you should have posted a message similar to the above on the
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Talk:Schauder basis#Schauder basis versus topological basis
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one can consider the associated step function <math: -->
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1, the '''complex interpolation space''' (''X''<sub: -->
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page, rather than modifying the article without consulting.
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One also says that ''f'' is '''absolutely integrable'''.
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hello, just wanted to say that your recent attention to
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1,\\0 &\mbox{otherwise.}\end{cases}</math: -->
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space]]s are reflexive, as are the ] for {{nowrap|1
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Hilbert spaces are reflexive. The ''L''<sup: -->
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1980:You appear to be eligible to vote in the current
1223:) be a compatible couple of Banach spaces. If 0
1188:) be a compatible couple of Banach spaces. If 0
1020:0} \, t^{\frac{1}{p}} f^{*}(t) & q = \infty.
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1793:)}} are isomorphic if and only if <math: -->
1765:List of unpaired brackets remaining on the page
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1121:1}}) if there exists a constant ''C'' such that
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958:List of unpaired brackets remaining on the page
863:\phi(t) = \begin{cases}1 \quad & 0 \leq t
844:\psi(t) = \begin{cases}1 \quad & 0 \leq t
834:List of unpaired brackets remaining on the page
1949:For your attention... (if you are still here)
1333:s, \ \ \text{and} \ \ f_1(x) = s f(x) / |f(x)
1166:s, \ \ \text{and} \ \ f_1(x) = s f(x) / |f(x)
628:{\displaystyle p_{n}(f)=\sup _{x\in }|f(x)|.}
8:
1855:\sup_{T \in F} \sup_{x \in U} \; \|T(x)\|_Y
1613:∞}}. More generally: all ] Banach spaces are
1816:] between ''C''(''K'') and ''C''(''L'') is
1678:and let ''t'' be a real number in {{nowrap|
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137:I hope you enjoy editing here and being a
16:I started here with a contribution to the
1953:This is probably a good question to you:
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1156:1, \ 1 \leq q < \infty,</math: -->
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1216:1, \ 1 \le q \le \infty.\,</math: -->
1327:f_1(x) = f(x) \ \ \text{if} \ \ |f(x)|
1160:f_1(x) = f(x) \ \ \text{if} \ \ |f(x)|
1494:\sum_{n=0}^{\infty} a_n </math: -->
984:\alpha\} \bigr) = \lambda \bigl( \{ t
203:Thanks to both of you for the work on
161:before the question. Again, welcome!
69:Knowledge talk:Wikiproject Mathematics
1866:spaces are reflexive when {{nowrap|1
1737:. I have automatically detected that
1557:. I have automatically detected that
1417:. I have automatically detected that
1339:| \ \ \text{otherwise}.</math: -->
1267:. I have automatically detected that
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1065:. I have automatically detected that
930:. I have automatically detected that
810:. I have automatically detected that
770:. I have automatically detected that
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1524:\int_0^{\infty} f_a dx</math: -->
1508:\rightarrow \mathbf{R}</math: -->
1200:1 and {{nowrap|1 ≤ ''q'' ≤ ∞}}, then
983:\mu \bigl( \{ x \in X : |f(x)| : -->
483:Hi, I have replied to your query at
1750:"s. If you have, don't worry, just
1570:"s. If you have, don't worry, just
1430:"s. If you have, don't worry, just
1280:"s. If you have, don't worry, just
1078:"s. If you have, don't worry, just
943:"s. If you have, don't worry, just
638:This gives C(a,b) the "topology of
1883:} is a basis for ''L''<sup: -->
320:) 21:33, 27 December 2008 (UTC) --
14:
2006:review the candidates' statements
1025:is contained in ''L''<sup: -->
685:compact operator on Hilbert space
679:compact operator on Hilbert space
274:Yes, the new version is better.
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1525:converges absolutely, converges
2012:. For the Election committee,
1982:Arbitration Committee election
1973:ArbCom elections are now open!
1782:\sum_{n=1}^{\infty} \|v_n\|_X
1640:1 + \varepsilon.</math: -->
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646:) to very abstract ones like
485:Talk:Topological vector space
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245:12:29, 18 November 2008 (UTC)
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195:08:04, 14 November 2008 (UTC)
180:07:31, 14 November 2008 (UTC)
112:The five pillars of Knowledge
1967:07:52, 23 October 2014 (UTC)
1836:\sup_{T \in F} \|T (x)\|_Y
1813:∞ and 1/''p'' + 1/''q'' = 1.
1800:\alpha^\omega.</math: -->
1676:of convexity]] δ<sub: -->
1462:\sum_{n=0}^{\infty} \|a_n\|
674:21:03, 29 January 2009 (UTC)
127:How to write a great article
103:to Knowledge! Thank you for
87:00:33, 2 November 2008 (UTC)
71:. Best regards and thanks,
54:13:26, 1 November 2008 (UTC)
30:23:32, 31 October 2008 (UTC)
2008:and submit your choices on
1006:\| f \|_{L^{p, q}} = \left\
739:Much thanks for the help.
503:20:49, 1 January 2009 (UTC)
2037:
2014:MediaWiki message delivery
1478:\varepsilon </math: -->
1219:''' Let (''X''<sub: -->
1184:''' Let (''X''<sub: -->
873:''n'', ''k''</sub: -->
697:04:25, 15 March 2009 (UTC)
1944:20:41, 27 July 2013 (UTC)
1749:by modifying 1 "<: -->
1719:08:21, 28 June 2013 (UTC)
1569:by modifying 2 "<: -->
1544:22:35, 21 June 2013 (UTC)
1429:by modifying 2 "<: -->
1279:by modifying 2 "<: -->
1124:'''Definition.''' For 0
1077:by modifying 2 "<: -->
942:by modifying 1 "<: -->
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822:by modifying 1 "<: -->
782:by modifying 2 "<: -->
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479:Topological vector spaces
1844:\ \sup_{T \in F} \|T\|
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1509:defined by <math: -->
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825:my operator's talk page
797:18:33, 8 May 2013 (UTC)
18:Vitali covering theorem
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508:Complete metric spaces
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1986:Arbitration Committee
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1523:. Then <math: -->
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1423:Absolute convergence
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421:With best wishes, --
1990:arbitration process
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1273:Interpolation space
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155:Knowledge:Questions
2002:arbitration policy
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1743:Banach space
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205:Hardy spaces
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74:siℓℓy rabbit
65:my talk page
62:
41:siℓℓy rabbit
36:my talk page
33:
15:
1733:Hello, I'm
1553:Hello, I'm
1413:Hello, I'm
1263:Hello, I'm
1061:Hello, I'm
990:0 : f^*(t)
926:Hello, I'm
806:Hello, I'm
766:Hello, I'm
343:infinite."
149:using four
1998:topic bans
1936:BracketBot
1735:BracketBot
1711:BracketBot
1555:BracketBot
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909:BracketBot
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789:BracketBot
787:. Thanks,
768:BracketBot
658:section.
159:{{helpme}}
139:Wikipedian
34:...And to
1994:site bans
1925:∞ so that
1739:your edit
1724:July 2013
1559:your edit
1419:your edit
1404:June 2013
1269:your edit
1067:your edit
932:your edit
812:your edit
772:your edit
409:ignorant.
257:Thenub314
172:Thenub314
141:! Please
1934:Thanks,
1893:('''T'''
1709:Thanks,
1534:Thanks,
1502:0,\infty
1389:Thanks,
1244:Thanks,
1042:Thanks,
1033:''r''}}.
907:Thanks,
757:May 2013
656:Examples
185:Thanks!
117:Tutorial
95:Welcome!
1791:'': -->
1374:\theta
1358:\theta
1317:\theta
1235:1, then
1210:\theta
1150:\theta
975:f^{*}:
689:Mct mht
654:in the
438:Jackzhp
349:Jackzhp
101:welcome
59:Welcome
1984:. The
1904:''p''
1872:''p''
1794:\beta
1747:syntax
1622:''p''
1607:''p''
1567:syntax
1516:n,n+1)
1427:syntax
1277:syntax
1229:''θ''
1075:syntax
940:syntax
850:1/2,\\
820:syntax
780:syntax
393:series
389:series
270:Arzela
151:tildes
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999:: -->
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209:linas
2018:talk
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22:Bdmy
1978:Hi,
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