A theory of generalized functions based on holomorphic semi-groups Part A: introduction and survey

✍ Scribed by J. de Graaf

• Publisher: Elsevier Science
• Year: 1983
• Weight: 633 KB
• Volume: 86
• Category: Article
• ISSN: 1385-7258
• DOI: 10.1016/s1385-7258(83)80018-3

✦ Synopsis

In a Hilbert space X consider the evolution equation du --.~/bl dt with .~ a nonnegative unbounded self-adjoint operator..J is the infinitesimal generator of a holomorphic semi-group. Solutions u(. ):(0, oo)~X of this equation are called trajectories. Such a trajectory may or may not correspond to an "initial condition at t = 0" in X. The set of trajectories is considered as a space of generalized functions. The test function space is defined to be