عنوان

Singularities of analytic functions and group representations

Number

TLets787369

Title Proper

Singularities of analytic functions and group representations

General Material Designation

[Thesis]

First Statement of Responsibility

Al Ameer, Amerah Ahmad M.

Subsequent Statement of Responsibility

Kisil, Vladimir

Name of Publisher, Distributor, etc.

University of Leeds

Date of Publication, Distribution, etc.

2019

Dissertation or thesis details and type of degree

Thesis (Ph.D.)

Text preceding or following the note

2019

Text of Note

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.

Al Ameer, Amerah Ahmad M.

Kisil, Vladimir

University of Leeds

Electronic name

p

[Thesis]

276903

a

Y