Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 1968 | Published
Journal Article Open

A Banach space of analytic functions for constant coefficient equations of evolution

Marsden, J.

Abstract

The space involved in the theory of equations of evolution (that is, the theory of semi-groups) are such that the infinitesimal generators are only densely defined. For the infinitesimal generator to be everywhere defined and smooth (that is, differentiable), one must work with a Frechet space. This is especially important in the non linear theory of Moser. If the spaces were Banach spaces, the theory would reduce to the classical Picard theory for ordinary differential equations. In fact in this case the existence theory is both simpler and more comprehensive, because we obtain the important fact that the flow is a diffeomorphism (the solutions depend smoothly, and not merely continuously on the initial data).This has other advantages too, since the theory for smooth flows on Banach manifolds is well developed.

Additional Information

© 1968 CANADIAN MATHEMATICAL SOC.

Attached Files

Published - Ma1968_2_.pdf

Files

Ma1968_2_.pdf
Files (95.0 kB)
Name Size Download all
md5:a55ba9244539d5b08a106eead4058183
95.0 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023