Prime and Semiprime Inner Functions

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

Prime and semiprime inner functions

Abstract This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided.

SEARCHING FOR HOPE IN SAMUEL BECKETT, EDWARD ALBEE, AND SAM SHEPARD

Reading absurdist plays as hopeful is rare because they are filled with portrayals of horror and despair. However, the tragedy of these plays can allow the audience to experience an atypical kind of hope, often during the final moments of the play. Though the conclusions of the plays are usually ambiguous, this ambiguity and lack of resolutiondoes not preclude hope. The characters persist through their suffering and react in ways that can allow a hopeful affect on the audience. The three absurdist playwrights, Samuel Beckett, Edward Albee, and Sam Shepard, express differing views of the tragic nature of the human condition. However, persistent through all of their work is the ability to view tragedy as having a hopeful affect on the audience. Though the plays do not necessitate a reading of hopefulness, their plays do not preclude this. These absurdist plays do not force the audience into despair, but instead leave open the option of experiencing an expectation and determination for life.