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Results tagged with real-analysis
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user 9833
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
4
votes
1
answer
282
views
A weak fragment of analysis?
Question: Is there a decidable theory sufficient to formulate and prove (many) theorems of classical analysis?
What I have in mind is a theory with two kinds of objects, reals (which are introduced a …
- 6,891
3
votes
0
answers
237
views
How to denote a partial derivative?
This question is related to Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix? and Suggestions for good notation .
When there are two f …
- 6,891
17
votes
2
answers
3k
views
The Riemann hypothesis as a problem in analysis
The recent post("Long-standing conjectures in analysis ... often turn out to be false") prompted me to think about a question which I have not given much though before: to what extent the Riemann hypo …
- 6,891
0
votes
An apparently simple question (behaviour at infinity of a power series)
If there is an uniform convergence, then, for example, $c_n=\sum_{k=0}^n a_kn^k$ will do. But no "reasonable" sequence will work in general, I agree with Loïc Teyssier on this. To say more, one has to …
- 6,891
2
votes
Closed-Form solution for system of simple nonlinear equations
(Not really an answer, but hopefully may be helpful.)
It is convenient to consider this as a problem of finding a solution of the equation
$$(N-2)x-\sum_i\delta_i\sqrt{x^2-d_i}=0,$$
for a given vect …
- 6,891
2
votes
Can we stay invertible while approximating linear maps in Sobolev spaces?
Consider the case $n=2$,
\begin{equation*}
A(x,y)=\left(
\begin{array}{cc}
x & -y \\
y & x
\end{array} \right)
\end{equation*}
This function is not just in a Sobolev space, it is analytic. Obviousl …
- 6,891
4
votes
Analytic approximations of smooth vector fields
I believe the most natural approach to this particular question is via Fourier analysis. In the periodic case we have the series
$$u(x)=\sum_{k\in\mathbb{Z}^3}u_k e^{2\pi i (k,x)},$$
and the condition …
- 6,891
30
votes
"Long-standing conjectures in analysis ... often turn out to be false"
The Riemann hypothesis is a conjecture in both analysis and number theory. Someone who tries to undermine it necessarily has to ignore the latter part or to declare it irrelevant. I am not suggesting …