User njguliyev - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T11:31:22Z http://mathoverflow.net/feeds/user/26107 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126420/functions-of-one-complex-variable-geometric-theory/126435#126435 Answer by njguliyev for functions of one complex variable: geometric theory njguliyev 2013-04-03T19:22:32Z 2013-04-03T19:22:32Z <p>Gamelin T.W. Complex analysis. Springer, 2001.</p> http://mathoverflow.net/questions/125655/spectral-theorem-for-self-adjoint-differential-operator-on-hilbert-space/125673#125673 Answer by njguliyev for Spectral theorem for self-adjoint differential operator on Hilbert space njguliyev 2013-03-26T21:37:42Z 2013-03-26T21:47:26Z <p>For differential (especially, for Sturm--Liouville) operators I would recommend Akhiezer, Glazman's "Theory of linear operators in Hilbert space" and Naimark's "Linear differential operators".</p> <p>In von Neumann's classical book "Mathematical foundations of quantum mechanics" the spectral theorem is stated very roughly.</p> http://mathoverflow.net/questions/125398/a-weakly-null-sequence/125404#125404 Answer by njguliyev for A weakly null sequence? njguliyev 2013-03-23T21:44:21Z 2013-03-23T21:44:21Z <p>No, this isn't true even for $f_n(x) = \sqrt{2} \sin n\pi x$. Then $g_n := \frac{F_n}{\|F_n\|} = \sqrt{\frac{2}{3}}(1-\cos n\pi x)$ and $\langle g_n, 1\rangle = \sqrt{\frac{2}{3}} \not\to 0$.</p> http://mathoverflow.net/questions/125139/dual-space-of-mathcalc-0a-b/125140#125140 Answer by njguliyev for Dual space of $\mathcal{C}_0[a,b]$ njguliyev 2013-03-21T09:53:06Z 2013-03-21T10:26:13Z <p>Each (bounded linear) functional on $C[a,b]$ is also a functional on $C_0[a,b]$. Each function $f \in C[a,b]$ can be written as $f(x) = f_0(x) + f(a) \cdot 1$, where $f_0 \in C_0[a,b]$. On the other hand, each functional on $C_0[a,b]$ can be extended to a functional on $C[a,b]$ (Hahn-Banach). Therefore the answer is $(C[a,b])^{\ast}/\mathbb{C}$. In terms of those functions of bounded variation, this means that we have to require those functions vanish at one more point.</p> http://mathoverflow.net/questions/105702/good-reference-for-the-construction-of-a-greens-functions-fur-the-sturm-liouville/118390#118390 Answer by njguliyev for Good reference for the construction of a Greens functions fur the Sturm-Liouville njguliyev 2013-01-08T20:15:52Z 2013-01-08T20:15:52Z <p>Levitan B.M., Sargsjan I.S. Sturm-Liouville and Dirac operators. Kluwer, 1991. xii+350 pp. ISBN: 0-7923-0992-8</p> <p>Section I.5 of this book contains a detailed construction of Green's function for the Sturm-Liouville problem.</p> http://mathoverflow.net/questions/118131/a-c-infty-function-on-a-submanifold-which-is-not-the-restriction-of-a-a-c-in/118133#118133 Answer by njguliyev for A $C^\infty$-function on a submanifold which is not the restriction of a a $C^\infty$ on $M$ njguliyev 2013-01-05T15:45:13Z 2013-01-06T17:28:06Z <p>You can take $M = \{ z \in \mathbb{C} \colon |z|=1\}$, $N = M \setminus \{1\}$ and $f(e^{i\varphi}) = \varphi$.</p> http://mathoverflow.net/questions/117415/old-books-still-used/117654#117654 Answer by njguliyev for Old books still used njguliyev 2012-12-30T17:37:56Z 2012-12-30T17:37:56Z <p>"Differential and integral calculus" (Russian) by G. M. Fichtenholz was first published in 1948. Recently (in 2009) its $9^{th}$ edition was published and this book is still used as the main calculus textbook at some universities.</p> http://mathoverflow.net/questions/20071/how-to-find-icm-talks/127523#127523 Comment by njguliyev njguliyev 2013-04-14T13:35:03Z 2013-04-14T13:35:03Z <a href="http://libgen.org/search?req=Proceedings+of+The+International+Congress+of+Mathematicians+2010&amp;nametype=orig&amp;column%5B%5D=title&amp;column%5B%5D=author&amp;column%5B%5D=series&amp;column%5B%5D=periodical&amp;column%5B%5D=publisher&amp;column%5B%5D=year" rel="nofollow">libgen.org/&hellip;</a> http://mathoverflow.net/questions/127401/sufficient-conditions-for-continuity-of-function-y-mapsto-min-x-0-y-phi Comment by njguliyev njguliyev 2013-04-12T20:43:11Z 2013-04-12T20:43:11Z $\forall \epsilon &gt; 0$, $\exists \delta &gt; 0$, $\forall x \in (x_0-\delta, x_0+\delta)$: $\phi(x) \in (\phi(x_0)-\epsilon, \phi(x_0)+\epsilon)$. So $\psi(y) \in (\phi(x_0)-\epsilon, \phi(x_0)+\epsilon)$ too, therefore $\psi(y) \to \phi(x_0)$. The same is true for all other points. http://mathoverflow.net/questions/126088/dual-space-to-subspace-and-projection Comment by njguliyev njguliyev 2013-03-31T10:03:33Z 2013-03-31T10:03:33Z Duplicate. <a href="http://mathoverflow.net/questions/125903/dual-space-to-subspace-which-behaves-like-l1" rel="nofollow" title="dual space to subspace which behaves like l1">mathoverflow.net/questions/125903/&hellip;</a> http://mathoverflow.net/questions/125139/dual-space-of-mathcalc-0a-b/125140#125140 Comment by njguliyev njguliyev 2013-03-21T12:52:15Z 2013-03-21T12:52:15Z Of course. I didn't notice that... http://mathoverflow.net/questions/48908/is-the-invariant-subspace-problem-interesting/120292#120292 Comment by njguliyev njguliyev 2013-01-30T20:51:47Z 2013-01-30T20:51:47Z <a href="http://aperiodical.com/2013/01/the-invariant-subspace-problem-solved-for-hilbert-space/" rel="nofollow">aperiodical.com/2013/01/&hellip;</a> http://mathoverflow.net/questions/119998/on-analytic-function-differentiable-on-the-circle-of-convergence-of-its-taylor-se Comment by njguliyev njguliyev 2013-01-27T16:08:57Z 2013-01-27T16:08:57Z and still there are a lot of errors like &quot;seris&quot;, &quot;doesnot&quot;, double &quot;is&quot; etc. :-) http://mathoverflow.net/questions/119504/sequence-inequality Comment by njguliyev njguliyev 2013-01-21T21:43:13Z 2013-01-21T21:43:13Z or $a_n = \frac{1}{n^2}$ and $b_1 = \frac{\pi^2}{6}$, $b_n = \frac{1}{n^3}$ $(n&gt;1)$ http://mathoverflow.net/questions/118747/operation-on-measurable-sets-in-lines-containing-an-interval Comment by njguliyev njguliyev 2013-01-12T18:20:42Z 2013-01-12T18:20:42Z What is $w$ and what is $p$?