He is known for his innovative work in a number of fields, such as prehomogeneous vector spaces and Bernstein Sato polynomials; and particularly for his hyperfunction theory.
12.
If a hyperfunction is the boundary value of a holomorphic function on a wedge, then its analytic wave front set lies in the dual of the corresponding cone.
13.
At Leipzig, with ophthalmologist Alfred Bielschowsky, he conducted studies on fusion and cyclodeviation in paresis of the superior oblique muscle as well as on congenital hyperfunction of the superior oblique muscle.
14.
The left-hand side of this equation may be understood either as the difference of the limits of " F " ?from the appropriate half-planes, or as a hyperfunction distribution.
15.
In the edge-of-the-wedge theorem, we have a distribution ( or hyperfunction ) " f " on the edge, given as the boundary values of two holomorphic functions on the two wedges.
16.
Since the zeroth cohomology group of any sheaf is simply the global sections of that sheaf, we see that a hyperfunction is a pair of holomorphic functions one each on the upper and lower complex halfplane modulo entire holomorphic functions.
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