| Title | Derivation-Invariant Subspaces of C∞ |
| Authors | Alexandru Aleman, Boris Korenblum |
| Alternative Location | http://www.heldermann-verla..., Restricted Access |
| Publication | Computational Methods and Function Theory |
| Year | 2008 |
| Volume | 8 |
| Issue | 1-2 |
| Pages | 493 - 512 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Heldermann |
| Abstract English | Let $C^\infty(a,b)$ be the Fr\'echet space of all complex-valued infinitely differentiable functions on a (finite or infinite) interval $(a,b)\subset\mathbb{R}$. Let ${L\subset C^\infty(a,b)}$ be a closed subspace such that $DL\subset L$, where $D=\frac{d}{dx}$. Then the spectrum $\sigma_L$ of $D$ on $L$ is either the whole complex plane, or a discrete possibly void set of eigenvalues $\lambda$, each one with some finite multiplicity $m_\lambda\in \mathbb{N}$ such that the monomial exponentials $e_{\lambda,j}(x)=x^j\exp(\lambda x)$, $0\leq j\leq m_\lambda-1$ belong to $L$. If the spectrum is void there is a relatively closed interval $I\subset (a,b)$ such that $L$ consists of those functions from $C^\infty(a,b)$ which vanish identically on $I$. The interval may reduce to a point in which case $L$ consists of the functions that vanish together with all their derivatives at that point. |
| Keywords | Fourier transform., nearly invariance, spectrum, Differentiation operator, |
| ISBN/ISSN/Other | ISSN: 16179447 |
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