dc.contributor.advisor Thangavelu, S dc.contributor.author Kumar, Manish dc.date.accessioned 2018-01-01T06:23:21Z dc.date.accessioned 2018-07-31T06:09:11Z dc.date.available 2018-01-01T06:23:21Z dc.date.available 2018-07-31T06:09:11Z dc.date.issued 2018-01-01 dc.date.submitted 2016 dc.identifier.uri https://etd.iisc.ac.in/handle/2005/2937 dc.identifier.abstract http://etd.iisc.ac.in/static/etd/abstracts/3799/G27800-Abs.pdf en_US dc.description.abstract 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. en_US dc.language.iso en_US en_US dc.relation.ispartofseries G27800 en_US dc.subject Lie Groups en_US dc.subject Vectors en_US dc.subject Complex Number en_US dc.subject Heisenberg Group en_US dc.subject Banach Space en_US dc.subject Lie Algebra en_US dc.subject.classification Mathematics en_US dc.title Analytic and Entire Vectors for Representations of Lie Groups en_US dc.type Thesis en_US dc.degree.name MS en_US dc.degree.level Masters en_US dc.degree.discipline Faculty of Science en_US
﻿