Characterization of the hypoelliptic convolution operators on ultradistributions.
Extremal plurisubharmonic functions of linear growth on algebraic varieties.
Induktive Limites gewichteter Räume stetiger und holomorpher Funktionen.
Entire functions on nuclear sequence spaces.
On the range of convolution operators on non-quasianalytic ultradifferentiable functions
Let denote the non-quasianalytic class of Beurling type on an open set Ω in . For the surjectivity of the convolution operator is characterized by various conditions, e.g. in terms of a convexity property of the pair and the existence of a fundamental solution for μ or equivalently by a slowly decreasing condition for the Fourier-Laplace transform of μ. Similar conditions characterize the surjectivity of a convolution operator between ultradistributions of Roumieu type whenever . These...
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse
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 .
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