Singularities of analytic functions and group representations

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" Singularities of analytic functions and group representations "
Al Ameer, Amerah Ahmad M. Kisil, Vladimir

Document Type	:	Latin Dissertation
Record Number	:	833675
Doc. No	:	TLets787369
Main Entry	:	Al Ameer, Amerah Ahmad M.
Title & Author	:	Singularities of analytic functions and group representations\ Al Ameer, Amerah Ahmad M.Kisil, Vladimir
College	:	University of Leeds
Date	:	2019
student score	:	2019
Degree	:	Thesis (Ph.D.)
Abstract	:	In this thesis, we demonstrate some connections between the coefficients of a Taylor series f(z)=∑∞n=0 aₙzⁿ and singularities of the function. There are many known results of this type; for example, counting the number of poles on the circle of convergence and doing convergence or overconvergence for f on any arc of holomorphy. Here, a new approach is proposed in which these kinds of results are extended by relaxing the classical conditions for singularities and convergence theorems. This is done by allowing the coefficients to be sufficiently small instead of being zero. The well-known theta function is an important example. Every point on the boundary of its domain of holomorphy is singular. This function is delivered from the covariant transform associated with the Heisenberg group representations. Therefore, we devote the rest of our present work to deal primarily with the covariant transform. We introduce three different forms of the Heisenberg group representations. The covariant transform allows us to construct intertwining operators related to L_2-type spaces between the representations of the Heisenberg group. The systematic usage of the covariant transform between different spaces on which the Heisenberg group representations act is another new contribution in this thesis.
Added Entry	:	Kisil, Vladimir
Added Entry	:	University of Leeds