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 spectrum of Carleman matrix bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 02/22/2009, 01:18 PM (This post was last modified: 02/22/2009, 01:23 PM by bo198214.) Hey Gottfried, did you ever thought about the spectrum of the Carleman matrix of $\exp_b$? For finite matrices the spectrum is just the set of eigenvalues. However for an infinite matrix or more generally for a linear operator $A$ on a Banach space the spectrum is defined as all values $\lambda$ such that $A-\lambda I$ is not invertible. We saw that the eigenvalues of the truncated Carleman matrices of $\exp$ somehow diverge. So it would be very interesting to know the spectrum of the infinite matrix. As this also has consequences on taking non-integer powers of those matrices. Or is the spectrum just complete $\mathbb{C}$ because $A$ is not invertible itself? « Next Oldest | Next Newest »

 Messages In This Thread spectrum of Carleman matrix - by bo198214 - 02/22/2009, 01:18 PM RE: spectrum of Carleman matrix - by Gottfried - 02/22/2009, 09:29 PM RE: spectrum of Carleman matrix - by bo198214 - 02/22/2009, 10:53 PM RE: spectrum of Carleman matrix - by Gottfried - 02/23/2009, 03:52 AM

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