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Results tagged with real-analysis
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user 5963
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
10
votes
Accepted
"sinc-ing" integral
Let $s(x) = \frac{\sin(\pi x)}{\pi x}$ be the normalized sinc function, $a_j' = \frac{a_j}{\pi}$ and $c = \frac{b+\sum_j a_j}{\pi}$. Then you want to compute $\pi\int_{-\infty}^\infty c s(cx)\prod_j …
- 43.2k
7
votes
On an example of an eventually oscillating function
Here's an unenlightening proof of part $1$, assuming you believe my computer's ability to multiply six-digit numbers correctly. If not you could do the $22$ six-digit multiplications by hand. If you …
- 8,501
0
votes
Formalism for moving from a metric space into a vector space for mathematical/statistical mo...
You may be interested in kernel methods, which are not exactly what you describe but have some of the properties you seem to be seeking. In particular they can be viewed as a way to use linear algebr …
- 8,501
7
votes
on the set of numbers generated by integer linear combination of two real numbers.
Yes, the set $X = a\mathbb{N} + b\mathbb{N}$ is order-isomorphic to $\mathbb{N}$.
For any positive real $k$ the set $X\cap [0,k]$ is finite. Indeed, to have $ap+bq \leq k$ for $p,q\in\mathbb{N}$ we …
- 8,501