= Solution
Take the real <L2 space> $\mathcal H=L^2((0,\infty),dt)$ and the <feature map>
$$
\varphi(x)(t)=\mathbf1_{(0,x]}(t).
$$
Each <indicator function> belongs to $\mathcal H$ because its squared <L2 norm> is $x<\infty$. Their <inner product> is the length of the overlapping intervals:
$$
\boxed{\langle\varphi(x),\varphi(x')\rangle=\int_0^\infty\mathbf1_{(0,x]}(t)\mathbf1_{(0,x']}(t)\,dt=\min(x,x')=k_1(x,x')}.
$$
This realizes $k_1$ as a <positive-semidefinite kernel>; it is also the <Brownian covariance kernel>.
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