Branching of singularities for degenerate hyperbolic operators and Stokes phenomena, II
Kazuo Amano, Gen Nakamura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1981
Recently, one of the authors revealed a closed connection between branching of singularities and Stokes phenomena for a certain class of degenerate hyperbolic operators ([2]).We generalize his result to the following type of degenerate hyperbolic linear partial differential operators P in Re (R" P= Pm_(t, x, Dt, Dx), i=O Pro(t, x, r, )= 1-[ (r--t2(t, x, )), i=l m-i Pm_(t, x, r, )= t(')P(t, x, )r --, j=O where Dt= a Dx=(DI Dxn)=( a 0 ) -t -X --X e N, z(i, ])=max(]--i, 0), ,(t, x, ) e C(RRR\O, R\O) are homogeneous o degree 1 with respect to , and P(t, x, ) e C(R R