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Analytic and Entire Vectors for Representations of Lie Groups

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Analytic and Entire Vectors for Representations of Lie Groups
 
Creator Kumar, Manish
 
Subject Lie Groups
Vectors
Complex Number
Heisenberg Group
Banach Space
Lie Algebra
Mathematics
 
Description We start with the recollection of basic results about differential manifolds and Lie groups. We also recall some preliminary terminologies in Lie algebra. Then we define the Lie algebra corresponding to a Lie group. In the next section, we define a strongly continuous representation of a Lie group on a Banach space. We further define the smooth, analytic and entire vectors for a given representation. Then, we move on to develop some necessary and sufficient criteria to characterize smooth, analytic and entire vectors. We, in particular, take into account of some specific representations of Lie groups like the regular representation of R, the irreducible representations of Heisenberg groups, the irreducible representations of the group of Affine transformations and finally the representations of non-compact simple Lie groups.
 
Contributor Thangavelu, S
 
Date 2018-01-01T06:23:21Z
2018-01-01T06:23:21Z
2018-01-01
2016
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2937
http://etd.ncsi.iisc.ernet.in/abstracts/3799/G27800-Abs.pdf
 
Language en_US
 
Relation G27800