Citation
Biyanov, Andrey Y. (1995) Evolution equations and semigroups of operators with the disjoint support property. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd09052007110700
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Let [...], [...] be locally compact Hausdorff spaces, [...], [...] Banach spaces.
Theorem. T is an operator in [...], [...] with the disjoint support property if and only if [...] open, [...] such that:
(1) [...].
(2) [...] compact, [...] compact, [...] with the following property: [...].
(3) [...]
[...].
Let X be a locally compact Hausdorff space, E a Banach space.
Theorem. [...] is a [...]group on [...](X,E) with the disjoint support property if and only if [...] a continuous flow, [...] a continuous cocycle of [...] such that [...].
There is a corresponding result about [...]semigroups on [...](X,E) with the disjoint support property, where semiflows and semicocycles play the roles of flows and cocycles respectively.
Suppose [...], X is either (a,b) or [a,b], where by [[...],b] we mean ([...],b], and by [a,[...]] we mean [a,[...]).
Theorem. Let [...] be a [...]group on [...](X) with the disjoint support property. Then [...] is the union of pairwise disjoint intervals [...], [...], where I is either finite or countable and [...]: [...] such that [...] = [...] : [...] is a homeomorphism and the corresponding group dual
[...].
The above theorem generalizes the wellknown result of A. Plessner that if [...] and [...], then f is absolutely continuous if and only if [...].
The following theorem generalizes the result of N. Wiener and R. C. Young about the behavior of measures on [...] under translation.
Theorem. Let [...] be a [...]group on [...](X) with the disjoint support property. Then [...]
lim sup[...],
where [...] is the component of in [...]. Moreover, if lim sup[...] = 1, then the last inequality becomes an equality.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  20 April 1995 
Record Number:  CaltechETD:etd09052007110700 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd09052007110700 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3339 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  11 Sep 2007 
Last Modified:  26 Dec 2012 02:59 
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