@schn when you say that you need $f\in C^{m+1}$, are they specifying an error of $O\!\left(x^{m+1}\right)$ because they want to include the $x^m$ term? That does not require that $f\in C^{m+1}$, but it makes things simpler.
@epsilon-emperor: The problem is to show $\int_T e^{int}\mu(dt)\xrightarrow{n\rightarrow\infty}$. All the acrobatics done in for the hint shows that it is enough to show this for real measures, i.e., enough to assume that $\mu$ is real. Why? because we prove that if $\int_Te^{-int}\mu(dt)$ converges to $0$, then $\int_Te^{-int}f(t)|\mu|(dt)$ converges to $0$ for all bounded (or integrable) $f$.
my high school wasn't strong on european history, i keep it simple and just learn what colors to hate.
in grad school they had an event for grad students and faculty. i took down all the signs and replaced them with verbatim copies that said NO GANG COLORS in a very large font at the bottom. i would do the same tomorrow.
fiddling with signs was a big part of my graduate school education. i can't grow up and i can't change.
i'd replace aspects of the wording with creative variations. i'd change the descriptions of the talks on the seminar schedule. it was a juvenile attempt to shock the bourgeoisie.
if you are educated in or work in a place that has a bulletin board, i recommend this form of behavior as way of jolting people out of the prison of reality.
i don't have this avenue anymore because of work from home.
i remember editing one seminar talk announcement simply by adding the following sentence: "Everyone at this talk is going to be given pills."
i think the countercultural spirit that stereotypically animated the times would have been consistent with my own spirit. there was probably bad stuff too.
the problem with these days is nobody wants to goof off and change all of the posters on three floors of a math building. people don't want to put the effort in. they ask, why are you doing that. why would anybody do that.
another seminar talk i changed, and i only did this with people giving talks whom i knew, was changed to "We are going to compete to see who can eat the largest amount of crab cakes."
that's what people saw as the description of the talk
another summary i changed was from whatever the talk was about, i think sympletic geometry, to "We're alone, we're always alone, and the world is dark and mean."
Yeah if the proof is too algebraic, I don't really care. I just want to build intuition as to why such a statement may be true (it's being used a lot in stuff that I am reading)
i'm not finding it immediately. my classes on representation theory were focused on infinite dimensional noncommutative algebras but i do think there is something.
my cell phone has lost contact with my company's email server and i can't decide if this is something i should talk to IT about or a gift from the universe.
i'll see if i have an infringing copy in my electronic archives. this is ringing some kind of bell but i do not have physical copies of the textbook anymore.
Suppose a torus $T=(\mathbb{C}^\ast)^n$ acts on a finite dimensional vector space $W$, and define for $m \in M$ ($M$ is the character lattice of $T$) the eigenspace $W_m$ by
$$W_m = \{w \in W \mid t\cdot w = \chi^m(t)w \text{ for all }t \in T \}$$
i.e. for $w \in W_m$ is a simultaneous eigenvect...
Problem:
Assume we have the following points:
$(x_0,y_0), (x_1,y_1), (x_2,y_2), (x_3,y_3)$ where $x_0 = -3$, $x_1 = -2$,
$x_2 = -1$ and $x_3 = 0$.
Given the function $f(x) = Ax^2 + Bx + C$
find the constants $A$,$B$ and $C$ such that
$f(0) = y_3$ and
$$d = \sum_{i = 0}^{2} (f(x_i) - y_{i})^2$$
is...
