PDE-PRESERVING PROPERTIES
Copyright policy )PDE-PRESERVING PROPERTIES
A continuous linear operator \(T\) on the space of entire functions in \(d\) variables is called PDE-preserving for a given set \(\mathbb{P}\subseteq\mathbb{C}[\xi_1,\ldots,\xi_d]\) of polynomials if \(T\ker P(D)\subseteq P(D)\) for all \(P\in\mathbb P\), where \(P(D)\) is the differential operator obtained by replacing each variable \(\xi_j\) by \(\partial/\partial z_j\) in \(P\). The author studies the properties and the structure of the algebra of PDE-preserving operators for \(\mathbb P\).
Hilbert's Nullstellensatz, Invariant subspaces of linear operators, Operations and polynomials in algebraic structures, primal algebras, General theory of partial differential operators, Fourier-Borel transform, exponential type, PDE-preserving operator, convolution operator, Algebras of operators on Banach spaces and other topological linear spaces, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), Algebraic structures, PDE-preserving hull, Operator algebras with symbol structure
Hilbert's Nullstellensatz, Invariant subspaces of linear operators, Operations and polynomials in algebraic structures, primal algebras, General theory of partial differential operators, Fourier-Borel transform, exponential type, PDE-preserving operator, convolution operator, Algebras of operators on Banach spaces and other topological linear spaces, Banach spaces of continuous, differentiable or analytic functions, Linear operators on function spaces (general), Algebraic structures, PDE-preserving hull, Operator algebras with symbol structure
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!