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PDE-PRESERVING PROPERTIES
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 Title & Authors
PDE-PRESERVING PROPERTIES
PETERSSON HENRIK;
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 Abstract
A continuous linear operator T, on the space of entire functions in d variables, is PDE-preserving for a given set of polynomials if it maps every kernel-set ker P(D), , invariantly. It is clear that the set of PDE-preserving operators for forms an algebra under composition. We study and link properties and structures on the operator side versus the corresponding family of polynomials. For our purposes, we introduce notions such as the PDE-preserving hull and basic sets for a given set which, roughly, is the largest, respectively a minimal, collection of polynomials that generate all the PDE-preserving operators for . We also describe PDE-preserving operators via a kernel theorem. We apply Hilbert`s Nullstellensatz.
 Keywords
PDE-preserving;PDE-preserving hull;basic;convolution operator;exponential type;Fourier-Borel transform;algebra;invariant;Hilbert`s Nullstellensatz;
 Language
English
 Cited by
1.
HYPERCYCLICITY ON INVARIANT SUBSPACES,;

대한수학회지, 2008. vol.45. 4, pp.903-921 crossref(new window)
1.
A hypercyclicity criterion with applications, Journal of Mathematical Analysis and Applications, 2007, 327, 2, 1431  crossref(new windwow)
2.
Hypercyclic sequences of PDE-preserving operators, Journal of Approximation Theory, 2006, 138, 2, 168  crossref(new windwow)
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