Partial differential operators on $L^p \left( {E^n } \right)$

Right inverses for partial differential operators on Fourier hyperfunctions

We characterize the partial differential operators P (D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω)-type estimate valid for the bounded holomorphic functions on the characteristic variety VP near R . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén–Lindelöf-type condition.

Commutative Partial Differential Operators

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. In particular, we address the existence of a “spectral variety” generalizing the spectral curve of the one dimension...

Right inverses for linear, constant coefficient partial differential operators on distributions over open half spaces

Results of Hörmander on evolution operators together with a characterization of the present authors [Ann. Inst. Fourier, Grenoble 40, 619 – 655 (1990)] are used to prove the following: Let P 2 C‰z1; . . . ; znŠ and denote by Pm its principal part. If P ÿ Pm is dominated by Pm then the following assertions for the partial differential operators P…D† and Pm…D† are equivalent for N 2 Snÿ1: (1) P…D...

The left (right) distributivity of semi-t-operators over 2-uninorms

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS