3 papers
math.AP2026
A completion of our earlier work on the Cauchy problem for non-effectively hyperbolic operators
Tatsuo Nishitani
For hyperbolic differential operators with non-effectively hyperbolic double characteristics, we study the relationship between the Gevrey well-posedness threshold for strong w…
math.AP2025
Notes on tangent bicharacteristics and ill-posedness of the Cauchy problem
Enrico Bernardi, Tatsuo Nishitani
We exhibit a family of second-order hyperbolic differential operators presenting spectral transition of the Hamilton map. As a consequence we prove that the Cauchy problem is not l…
math.AP2025
Geometric results for hyperbolic operators with spectral transition of the Hamilton map
Enrico Bernardi, Tatsuo Nishitani
In this paper we study a class of non-effectively hyperbolic operators vanishing of order 2 on a manifold, on a sub-region of which the spectral structure of the Hamilton map chang…