You are here
PSEUDOQUOTIENTS: CONSTRUCTION, APPLICATIONS, AND THEIR FOURIER TRANSFORM
 Date Issued:
 2008
 Abstract/Description:
 A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the noninjective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a welldefined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. We answer some questions about the extension properties. One family of these questions involves assuming a structure (algebraic or topological) on a set and asking if the set of pseudoquotients generated has the same structure. A second family of questions looks at maps between two sets and asks if there is an extension of that map between the corresponding pseudoquotients? If so, do the properties of the original map survive the extension? The result of our investigations on the abstract setting will be compared with some wellknown spaces of pseudoquotients and Boehmians (a particular case of noninjective pseudoquotients). We will show that the conditions discussed in the first part are satisfied and we will use that to reach conclusions about our extension spaces and the extension maps. The Fourier transform is one of the maps that we will continuously revisit and discuss. Finally many spaces of Boehmians have been introduced where the initial set is a particular class of functions on either locally compact groups R and or a compact group such as a sphere. The natural question is, can we generalize the construction to any locally compact group. In some previous work such construction is discussed, however here we go further; we use characters and define the Fourier transform of integrable and square integrable Boehmians on a locally compact group. Then we discuss the properties of such transform.
Title:  PSEUDOQUOTIENTS: CONSTRUCTION, APPLICATIONS, AND THEIR FOURIER TRANSFORM. 
0 views
0 downloads 

Name(s): 
Khosravi, Mehrdad, Author Mikusinski, Piotr, Committee Chair University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2008  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the noninjective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a welldefined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. We answer some questions about the extension properties. One family of these questions involves assuming a structure (algebraic or topological) on a set and asking if the set of pseudoquotients generated has the same structure. A second family of questions looks at maps between two sets and asks if there is an extension of that map between the corresponding pseudoquotients? If so, do the properties of the original map survive the extension? The result of our investigations on the abstract setting will be compared with some wellknown spaces of pseudoquotients and Boehmians (a particular case of noninjective pseudoquotients). We will show that the conditions discussed in the first part are satisfied and we will use that to reach conclusions about our extension spaces and the extension maps. The Fourier transform is one of the maps that we will continuously revisit and discuss. Finally many spaces of Boehmians have been introduced where the initial set is a particular class of functions on either locally compact groups R and or a compact group such as a sphere. The natural question is, can we generalize the construction to any locally compact group. In some previous work such construction is discussed, however here we go further; we use characters and define the Fourier transform of integrable and square integrable Boehmians on a locally compact group. Then we discuss the properties of such transform.  
Identifier:  CFE0002186 (IID), ucf:47893 (fedora)  
Note(s): 
20080501 Ph.D. Sciences, Department of Mathematics Doctorate This record was generated from author submitted information. 

Subject(s): 
Boehmians pseudoquotients generalized quotients Levy measures Mikusinski 

Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0002186  
Restrictions on Access:  public  
Host Institution:  UCF 