# 2024/06/27

## The reproducing kernel beer problems

What follows is a list of problems initated in 2024 where first
solutions are rewarded with beer!
- Find a kernel such that
*k*_{y}
is unbounded.

**(**~~1B~~: Chris Felder 2024/06/25)

There are numerous examples,
one prominent is the kernel for the Segal-Bargman space.

- If the kernel functions explode on the diagonal of a sequence,
do the normalized kernel functions tend to 0 along that
sequence?

**(**~~1B~~: Chris Felder 2024/06/26)

- Number 2. but each kernel function should be linearly
independent.

**(**~~2B~~: Frej Dahlin and Chris Felder 2024/06/27)

Use the counter example of 2. but add the Szegő kernel.

- Suppose that each kernel function is linearly independent,
form the pseduo hyperbolic metric with respect to the kernel.
Is
*X* complete under this metric?

**(1B)**