#### Presentation Title

Extension of Nevanllina-Pick Theorem Interpolation Theorem to Various Subalgebras of Bounded Analytic Functions

#### Presentation Type

Event

#### Full Name of Faculty Mentor

Debandra Benjade

#### Major

Applied Mathematics

#### Presentation Abstract

Let π² be a subset of the set of positive integers and D be the open unit disk in the complex plane. Define, **π―βπ²(π«) = {π βπ―β(π«): ππ(π)=π , for all π βπ²}**. It is not necessary that all the subsets K form algebra π―βπ²(π«), for example take the set K = {2}. We consider those set K for which π―βπ²(π«) is algebra under the usual product of functions. In this talk, we extend Nevanlinna-Pick interpolation theorem π―βπ²(π«).

#### External Presentation

1

#### Location

Brittain Hall, Room 114

#### Start Date

17-4-2019 4:10 PM

#### End Date

17-4-2019 4:30 PM

#### Disciplines

Applied Mathematics

#### Recommended Citation

Dunivin, Jeremiah, "Extension of Nevanllina-Pick Theorem Interpolation Theorem to Various Subalgebras of Bounded Analytic Functions" (2019). *Undergraduate Research Competition*. 18.

https://digitalcommons.coastal.edu/ugrc/2019/oral/18

Extension of Nevanllina-Pick Theorem Interpolation Theorem to Various Subalgebras of Bounded Analytic Functions

Brittain Hall, Room 114

Let π² be a subset of the set of positive integers and D be the open unit disk in the complex plane. Define, **π―βπ²(π«) = {π βπ―β(π«): ππ(π)=π , for all π βπ²}**. It is not necessary that all the subsets K form algebra π―βπ²(π«), for example take the set K = {2}. We consider those set K for which π―βπ²(π«) is algebra under the usual product of functions. In this talk, we extend Nevanlinna-Pick interpolation theorem π―βπ²(π«).