User contributions for Hbghlyj

11:0311:03, 18 February 2025 diff hist +123‎ Mittag-Leffler's Expansion Theorem ‎ Add a BookReference current

11:1411:14, 24 January 2025 diff hist +719‎ N Talk:Irrational Number Space is Complete Metric Space ‎ →‎Alternative proof is to show that the irrationals are homeomorphic to $ω^ω$ via continued fractions: new section current
11:0611:06, 24 January 2025 diff hist +7‎ Irrational Number Space is Complete Metric Space ‎ The sentence "$\struct {\R \setminus \Q, \tau_d}$ is a complete metric space" is not in the original book. I think the sentence "$\struct {\R \setminus \Q, \tau_d}$ is a complete metric space" is slightly incorrect because you cannot say "a topology is a metric space" since a topology doesn't come with a unique metric, so it is better to write "The topology is a completely metrizable space"
10:2510:25, 24 January 2025 diff hist +127‎ Irrational Number Space is Complete Metric Space ‎ r_i is not defined in the proof.

19:1819:18, 21 December 2024 diff hist +17‎ m Definition:Acyclic Resolution ‎ Surround xymatrix with <nowiki> current

11:5411:54, 25 November 2024 diff hist +155‎ Bounds for Weierstrass Elementary Factors ‎No edit summary current

00:1900:19, 6 November 2024 diff hist +259‎ Definition:Sobolev Space ‎ explained {{explain|Presumably the "Sobolev space on $\map {L^2} {a, b}$"?}}
00:1100:11, 6 November 2024 diff hist +29‎ Friedrichs' Inequality ‎ Added category current

19:3919:39, 5 November 2024 diff hist 0‎ Friedrichs' Inequality ‎ According to Wikipedia https://en.wikipedia.org/wiki/Friedrichs%27s_inequality we should have k = 1 in W^{k,p} in Friedrichs's inequality

16:3516:35, 28 October 2024 diff hist +3‎ m Reverse Young's Inequality for Products ‎ fix a typo (forget minus sign)
16:3116:31, 28 October 2024 diff hist +25‎ m Reverse Young's Inequality for Products ‎ rename File
15:0615:06, 28 October 2024 diff hist +127‎ File:Reverse Young Inequality 3.svg ‎No edit summary Tag: Reverted
10:5210:52, 28 October 2024 diff hist +927‎ Reverse Young's Inequality for Products ‎ Add geometric proof
10:4910:49, 28 October 2024 diff hist +388‎ N File:Reverse Young Inequality 3.svg ‎ <code>\begin{tikzpicture} \fill[red!50](.8,0)--plot[domain=.8:1/1.7](\x,1/\x)-|(0,0); \draw(0,0)rectangle(.8,1.7); \node at(.8,0)[below]{$a$}; \node at(0,1.7)[left]{$b$}; \draw[->] (-0.2,0)--(2.2,0) node[right] {$x$}; \draw[->] (0,-0.2)--(0,2.7) node[above] {$y$}; \draw[color=blue,domain=.4:2.5] plot (\x,1/\x); \node at(1,1.2)[right]{$y=x^{p-1}$}; \end{tikzpicture}</code>
10:4510:45, 28 October 2024 diff hist +394‎ N File:Reverse Holder's Ineq Proof Integral 2.svg ‎ <code>\begin{tikzpicture} \fill[red!50](1/1.7,1.7)plot[domain=1/1.7:.4](\x,1/\x)-|(0,1.7); \draw(0,0)rectangle(.8,1.7); \node at(.8,0)[below]{$a$}; \node at(0,1.7)[left]{$b$}; \draw[->] (-0.2,0)--(2.2,0) node[right] {$x$}; \draw[->] (0,-0.2)--(0,2.7) node[above] {$y$}; \draw[color=blue,domain=.4:2.5] plot (\x,1/\x); \node at(1,1.2)[right]{$x=y^{-q-1}$}; \end{tikzpicture}</code> current
10:4010:40, 28 October 2024 diff hist +411‎ N File:Reverse Holder's Ineq Proof Integral 1.svg ‎ <code>\begin{tikzpicture} \fill[red!50](.8,0)--(.8,1.7)plot[domain=.8:.4](\x,1/\x)--(0,1/.4)--(0,0)--(.8,0); \draw(0,0)rectangle(.8,1.7); \node at(.8,0)[below]{$a$}; \node at(0,1.7)[left]{$b$}; \draw[->] (-0.2,0)--(2.2,0) node[right] {$x$}; \draw[->] (0,-0.2)--(0,2.7) node[above] {$y$}; \draw[color=blue,domain=.4:2.5] plot (\x,1/\x); \node at(1,1.2)[right]{$y=x^{p-1}$}; \end{tikzpicture}</code> current
10:3010:30, 28 October 2024 diff hist +328‎ N File:Reverse Holder's Ineq.svg ‎ <code>\begin{tikzpicture} \draw(0,0)rectangle(.8,1.7); \node at(.8,0)[below]{$a$}; \node at(0,1.7)[left]{$b$}; \draw[->] (-0.2,0)--(2.2,0) node[right] {$x$}; \draw[->] (0,-0.2)--(0,2.2) node[above] {$y$}; \draw[color=blue,domain=.4:2.5] plot (\x,1/\x); \node at(1,1.2)[right]{$y=x^{p-1}$}; \end{tikzpicture}</code> current
09:5609:56, 28 October 2024 diff hist +1‎ m Reverse Hölder's Inequality for Sums ‎ fix LaTeX error current