Sequence space representations for (FN)-algebras of entire functions modulo closed ideals
Characterization of smooth, compact algebraic curves in ℝ²
A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties
For complex algebraic varieties V, the strong radial Phragmén-Lindelöf condition (SRPL) is defined. It means that a radial analogue of the classical Phragmén-Lindelöf Theorem holds on V. Here we derive a sufficient condition for V to satisfy (SRPL), which is formulated in terms of local hyperbolicity at infinite points of V. The latter condition as well as the extension of local hyperbolicity to varieties of arbitrary codimension are introduced here for the first time. The proof of the main result...
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Each Non-Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse.
Plurisubharmonic functions with logarithmic singularities
To a plurisubharmonic function on with logarithmic growth at infinity, we may associate the Robin function defined on , the hyperplane at infinity. We study the classes , and (respectively) of plurisubharmonic functions which have the form and (respectively) for which the function is not identically . We obtain an integral formula which connects the Monge-Ampère measure on the space with the Robin function on . As an application we obtain a criterion on...
Analyse des réponses des étudiants à un questionnaire relatif au mémoire de recherche de la maîtrise en administration des affaires
Sur les systèmes d'équations différence-différentielles
Étant donné un système d’équations différence-différentielles à coefficients constants en deux variables, où les retards sont commensurables, de la forme : , , si le système n’est pas redondant (i.e. est discrète dans ), toute solution du système admet une représentation , où , et est une solution du système . La série est de plus convergente dans après un groupement de termes indépendant de la solution .
Whitney's extension theorem for non-quasi-analytic classes of ultradifferentiable functions.
This note can be considered as a long summary of the invited lecture given by J. Bonet in the Second Functional Analysis Meeting held in Jarandilla de la Vega (Cáceres) in June 1980 and it is based on our joint article [2], which will appear in Studia Mathematica. (...) The main result of the paper [2] is the characterization of those weight functions for which the analogue of Whitney's extension theorem holds.
Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.
The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood...
A new characterization of the analytic surfaces in that satisfy the local Phragmén-Lindelöf condition
We prove that an analytic surface in a neighborhood of the origin in satisfies the local Phragmén-Lindelöf condition at the origin if and only if satisfies the following two conditions: (1) is nearly hyperbolic; (2) for each real simple curve in and each , the (algebraic) limit variety satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure -dimensional analytic variety to satisify .
Spectral synthesis and the Pompeiu problem
It is shown that every closed rotation and translation invariant subspace of or , , is of spectral synthesis, i.e. is spanned by the polynomial-exponential functions it contains. It is a classical problem to find those measures of compact support on with the following property: (P) The only function satisfying for all rigid motions of is the zero function. As an application of the above result a characterization of such measures is obtained in terms of their Fourier-Laplace transforms....
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 .
Characterization of global Phragmén-Lindelöf conditions for algebraic varieties by limit varieties only
For algebraic surfaces, several global Phragmén-Lindelöf conditions are characterized in terms of conditions on their limit varieties. This shows that the hyperbolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in three variables in Beurling classes of ultradifferentiable functions.
Lattice modules having small cofinite irreducibles.
-systems in local Noether lattices.
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