Boehmians on manifolds.
A class of distributions supported by certain noncompact regular sets K are identified with continuous linear functionals on . The proof is based on a parameter version of the Seeley extension theorem.
Solving a problem of L. Schwartz, those constant coefficient partial differential operators are characterized that admit a continuous linear right inverse on or , an open set in . For bounded with -boundary these properties are equivalent to being very hyperbolic. For they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial .
The commutative neutrix convolution product of the functions and is evaluated for and all . Further commutative neutrix convolution products are then deduced.