Exercises
[0F2](Proposed on 2022-12) Find two examples of \(a_{i,j}:{\mathbb {N}}Γ {\mathbb {N}}β {\mathbb {R}}\)
such that, for each \(i\), \(β_ j a_{i,j} =0\), while for each \(j\), \(β_ i a_{i,j} =β\);
such that, for each \(i\), \(β_ j a_{i,j} =0\), while for each \(j\), \(β_ i a_{i,j} =1\).
Can you find examples where moreover we have that \(|a_{i,j}|β€ 1\) for every \(i,j\)? [ [0F3]]