7
votes
2answers
323 views
Growth of the “cube of square root” function
Hello all, this question is a variant (and probably a more difficult one)
of a (promptly answered ) question that I asked here, at http://mathoverflow.net/questions/18054/is-it-tru …
6
votes
5answers
315 views
Geometric group theory and analysis
Geometric group theory is mainly concerned with topological and geometric properties of groups, spaces on which they act etc., so the ideas employed in GGT are mainly algebraic/geo …
14
votes
7answers
842 views
How to solve f(f(x)) = cos(x) ?
I found the following interesting equation on some web page I cannot remember:
$f(f(x))=cos(x)$
Out of curiosity I tried to solve it, but realized that I do not have a clue how t …
3
votes
4answers
388 views
Difference between measures and distributions
On the one hand, Wikipedia suggests that every distribution defines a Radon measure:
http://en.wikipedia.org/wiki/Distribution_(mathematics)#Functions_as_distributions
On the o …
2
votes
5answers
468 views
Way to memorize relations between the Sobolev spaces?
Consider the Sobolev spaces $W^{k,p}(\Omega)$ with a bounded domain $\Omega$ in n-dimensional Euclidean space. When facing the different embedding theorems for the first time, one …
4
votes
2answers
101 views
How to find a solution to a particular Bottcher equation
Functional equations of the form $f(g(x))=(f(x))^p$, where $g(x)$ is known, is called Bottcher equation. Generally, we have only asymptotic formula for the solution $f(x)$ under ce …
9
votes
1answer
219 views
Path integrals, localisation
Physicists use the "Atiyah-Bott formula" for path "integrals" (for instance the supersymmetric proof of the Atiyah-Singer index theorem. Is there some way to make atleast some of t …
2
votes
1answer
151 views
Can we find an l-2 sequence if we know all l-p norms?
I'm wondering if there is a way to approximate the first $M$ terms of a non-increasing $\ell^2$ sequence ${c_n}$ if we know
$|c|_p^p = \sum c_n^p$ for $p=2,3,4,\dots$?
I've tri …
11
votes
12answers
877 views
How helpful is non-standard analysis?
So, I can understand how non-standard analysis is better than standard analysis in that some proofs become simplified, and infinitesimals are somehow more intuitive to grasp than e …
0
votes
1answer
62 views
How to prove that rational functions satisfy a Lipschitz condition in the *chordal metric*?
How can one show that rational functions satisfy a Lipschitz condition in the chordal metric on the Riemann sphere?
15
votes
79answers
4k views
Undergraduate Level Math Books
What are some good undergraduate level books, particularly good introductions to (Real and Complex) Analysis, Linear Algebra, Algebra or Differential/Integral Equations (but books …
7
votes
1answer
126 views
Hausdorff Dimension and Holder Continuity
Suppose we have a curve γ : [0,1] -> ℝn. It is well known that if this curve is Holder continuous for some exponent α then the Hausdorff dimension of γ[0, …
0
votes
1answer
81 views
the Cech-cohomology of the sheaf of germs of plurisubharmonic functions defined on a domain in C^n
we all know that if we consider the sheaf of germs of a holomorphic functions defined on a domain in C^n,we have too many beautiful theorems characterizing the geometry of the dom …
3
votes
0answers
191 views
A conjecture on matrix singular value inequality.
Singular inequalities are generally difficult to prove. Based on a sufficient numerical experiment, I propose the following conjecture, which has an interesting background. So far …
1
vote
2answers
169 views
what is summation in the sense of a principal value?
In one paper I saw this equality:
$$\sum_{\eta=-\infty}^{\infty}\frac{z}{(z+\eta)}=\pi z\cot(\pi z)$$
which is the same as
$$\sum_{\eta=-\infty}^{\infty}\frac{1}{(z+\eta)}=\pi …
