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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

0 votes
1 answer
61 views

Is the difference between polyfits for two data series equivalent to the polyfit of the diff...

Suppose that we have two series of data points $a(x)$ and $b(x)$ with the same domain of definition for $x$, and we fit two polynomial functions $f(x)$ and $h(x)$ (of the same order $n$) to them, resp …
nino's user avatar
  • 147
8 votes
3 answers
3k views

The mean of points on a unit n-sphere $S^n$

A unit n-sphere is defined as $$\mathcal{S}^n = \{\mathbf{p} \in \mathbb{R}^{n+1}: \|\mathbf{p}\| = 1\}$$ The distance between two points $\mathbf{p}$, $\mathbf{q}$ on $\mathcal{S}^n$ is the great-ci …
nino's user avatar
  • 147
6 votes
1 answer
1k views

On proof of the conditionally negative definiteness of a kernel

Let the kernel be $f(\mathbf{x},\mathbf{y}) = \arccos(\mathbf{x}^T \mathbf{y})$, where $\mathbf{x}$ and $\mathbf{y}$ are $\ell_2$ normalized vectors of the same dimensionality, and $\arccos(\cdot): [- …
nino's user avatar
  • 147