All Questions

Let $\Delta=\{(t,s):\ 0<s\leq t\leq1\}$, and suppose $k:\Delta\to\mathbb R$ and $f:(0,1]\to\mathbb R$ are continuous. Further assume that for every $t\in(0,1]$, the function $k(t,\cdot):(0,t]\to\...

Letting $D:=\{(x,y):\ 0\leq x\leq y\leq1 \text{ and } y>0\}$, I have a continuous function $k:D\to[0,\infty)$ that satisfies some properties that I list below. I'm interested in continuous and ...

In order to solve a boundary problem for a conducting hemisphere, the following matrix equation arises (derived from the boundary condition on the curved part of the surface) where we must solve for ...

Consider the functional equation $$ g\left(a\right) = \int_0^1 \frac{e^{c(a,h)+f(h)}}{1+e^{c(a,h)+f(h)}}dh $$ and this holds for all $a$. $g(a)$ and $c(a,h)$ are known functions on a continuous ...

I was working around with the fractional Fourier transform (FRFT) when the mathematics undergrad found out, by brute-force computations, that the derivative of the FRFT with respect to the parameter ...

I really want to prove the statement in the title but I'm struggling with it. Here my current state: Proof via contradiction. Let $\mathcal{H}$ be a RKHS with two reproducing kernels $k$ and $\hat{k}$ ...