• Login
    View Item 
    •   Home
    • University of Alaska Fairbanks
    • UAF Graduate School
    • Mathematics and Statistics
    • View Item
    •   Home
    • University of Alaska Fairbanks
    • UAF Graduate School
    • Mathematics and Statistics
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of Scholarworks@UACommunitiesPublication DateAuthorsTitlesSubjectsTypeThis CollectionPublication DateAuthorsTitlesSubjectsType

    My Account

    Login

    First Time Submitters, Register Here

    Register

    Statistics

    Display statistics

    Linear partial differential equations and real analytic approximations of rough functions

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    Barry_T_2017.pdf
    Size:
    3.663Mb
    Format:
    PDF
    Download
    Author
    Barry, Timothy J.
    Chair
    Rybkin, Alexei
    Committee
    Avdonin, Sergei
    Faudree, Jill
    Keyword
    Differential equations, Partial
    Fourier transformations
    Initial value problems
    Metadata
    Show full item record
    URI
    http://hdl.handle.net/11122/7860
    Abstract
    Many common approximation methods exist such as linear or polynomial interpolation, splines, Taylor series, or generalized Fourier series. Unfortunately, many of these approximations are not analytic functions on the entire real line, and those that are diverge at infinity and therefore are only valid on a closed interval or for compactly supported functions. Our method takes advantage of the smoothing properties of certain linear partial differential equations to obtain an approximation which is real analytic, converges to the function on the entire real line, and yields particular conservation laws. This approximation method applies to any L₂ function on the real line which may have some rough behavior such as discontinuities or points of nondifferentiability. For comparison, we consider the well-known Fourier-Hermite series approximation. Finally, for some example functions the approximations are found and plotted numerically.
    Description
    Thesis (M.S.) University of Alaska Fairbanks, 2017
    Table of Contents
    Chapter 1. Introduction -- Chapter 2. Heat equation -- Chapter 3. Airy equation -- Chapter 4. Hermite polynomials -- Chapter 5. Conclusion -- References.
    Date
    2017-08
    Type
    Thesis
    Collections
    Mathematics and Statistics

    entitlement

     
    ABOUT US|HELP|BROWSE|ADVANCED SEARCH

    The University of Alaska Fairbanks is an affirmative action/equal opportunity employer and educational institution and is a part of the University of Alaska system.

    ©UAF 2013 - 2023 | Questions? ua-scholarworks@alaska.edu | Last modified: September 25, 2019

    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.