All Questions

Let $f(x)$ be a positive definite function on $x \in R^d$. Assume $f(x)$ is radial , so $f(x)$ is a function of $|x|$, let's say $g(|x|):=f(x)$. How can I show that $g(|x|^\gamma)$ is positive ...

I have the $N$x$N$ matrix below where $N$ is a power of 2 (usually 64 or 256) and $\omega = 2\pi/N$. What is its largest eigenvalue? $\begin{bmatrix} 2 & 1 & 0 & 0 & \cdots & 0 &...

I am reposting this question from Cross Validated as I have not received any responses. While reading this book, I got stuck on page 266 where the authors found the spectral measure $F(du)$ of the ...