Classification of homogeneous distributions

Question

On page 92 of these notes, there is a discussion on how to find the fundamental solution to the D'Alembertian operator. It is firstly proposed that $c_n(t^2 - |x|^2 )^{-(n-1)/2}$ may be a good candidate. Then the author says that we can use the homogeneous family of distributions $j_a$ to get a homogeneous distribution that agrees with the above function in $t>|x|$.

However, I am unable to find the definition of $j_a.$

Could anyone give me a reference/clue on what result we are using here?

These are Riesz distributions. They are mentioned in these answers, with references. The main one is Gelfand-Shilov Generalized Functions I. — Igor Khavkine, May 03 '21 at 01:10

score 2 · Accepted Answer · answered May 03 '21 at 02:50

2

In sergiu's notes that you referred to, $j_a$ is defined in Definition 3.2 on Page 65. See equation (134).

answered May 03 '21 at 02:50

Willie Wong

37,551

Thank you very much for pointing out! Somehow I have overlooked this. – Ma Joad May 03 '21 at 07:25
No worries; that particular missing cross reference was already a small "bug" when I was a student 15 years ago. – Willie Wong May 03 '21 at 13:47

Classification of homogeneous distributions

1 Answers1