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Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

José BonetReinhold Meise — 2008

Studia Mathematica

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ( ω ) ( ) of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on ( ω ) [ a , b ] for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on ( ω ) ( ) .

Extension and lacunas of solutions of linear partial differential equations

Uwe FrankenReinhold Meise — 1996

Annales de l'institut Fourier

Let K Q be compact, convex sets in n with K and let P ( D ) be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of P ( D ) in the space ( K ) of all C -functions on K extends to a zero solution in ( Q ) resp. in ( n ) . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of P in n and in terms of for P ( D ) with lacunas.

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