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Jan
30
answered Feynman lectures, Volume I, chapter 13-4
Jan
18
awarded  Yearling
Sep
24
comment Example of an additive but not linear map beetween real topological linear spaces
Hi, the notation $\mathbb Q [\sqrt {2}]$ stands for the rational multiples of the equivalence class “$\sqrt 2$”, is that right? Moreover, is the point that $f(\sqrt 2 x)=-\sqrt 2 f(x)$ for real $x$?
Sep
24
comment Example of an additive but not linear map beetween real topological linear spaces
@IttayWeiss altough my knowledge of infinite dimensional vector spaces is very restricted, yes.
Sep
24
asked Example of an additive but not linear map beetween real topological linear spaces
Sep
14
comment Integrate and measure problem.
However, I think that the first version of the post (before I started to confuse things up) was the right one: the integral on $|f|\leq 1$ must be evaluated via the monotone convergence theorem (negating before and after the integral, and defining $-\log 0=\infty$): this is so because the hypothesis of the DCT, that is, that the pointwise limit is a complex measurable function, is not met where $f(x)=0$, and this set could have positive measure.
Sep
14
comment Integrate and measure problem.
Hi robjohn, thank you. I understand the point, on $|f|\leq 1$ the pointwise limit of $g_p(f)$ isn't necessarily a complex measurable function (if $f(x)=0$).
Sep
13
comment Integrate and measure problem.
Sorry, I meant the $p_0$ of the OP.
Sep
13
comment Integrate and measure problem.
Hi robjohn, do we really need to split the integral in two parts, in in (2f)? It looks to me that we can apply dominated convergence to the whole integral, using $g_r(|f|)$.
Aug
18
awarded  Popular Question
Jun
25
comment Is the Cauchy-Schwarz inequality ever used in Physics?
That's the perfect example! See, for instance, Sakurai “Modern Quantum Mechanics”, 1.4 .
Apr
15
comment How to estimate the axis of symmetry for an even function with error?
You are welcome! If the large error is on the $y_i$'s, I've added a second (maybe more practical) method that could work.
Apr
15
revised How to estimate the axis of symmetry for an even function with error?
added 671 characters in body
Apr
15
answered How to estimate the axis of symmetry for an even function with error?
Apr
8
awarded  Enlightened
Apr
7
awarded  Nice Answer
Mar
5
answered Show that $A =\left(\begin{smallmatrix}41&12\\12&34\end{smallmatrix}\right)$ is symmetric positive definite
Mar
4
comment Show that $A =\left(\begin{smallmatrix}41&12\\12&34\end{smallmatrix}\right)$ is symmetric positive definite
Hint for alternative method: is there any relationship beetween $A$'s eigenvalues and quantities like, for example $\det A$?
Jan
31
accepted Differential of the inversion of Lie group
Jan
22
awarded  Peer Pressure