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Outer Approximation of the Spectrum of a Fractal Laplacian

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003778/00001

Material Information

Title: Outer Approximation of the Spectrum of a Fractal Laplacian
Physical Description: Book
Language: English
Creator: Goff, Stacey
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2007
Publication Date: 2007

Subjects

Subjects / Keywords: Fractal
Laplacian
Partial Differential Equations (PDE)
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The Neumann spectrum of a Laplacian on a fractal K in the plane is approximated as a renormalized limit of the Neumann spectra of the standard Laplacian on a sequence of domains which approximate K from the outside. Eigenvalues and eigenfunctions are approximated numerically for lower portions of the spectrum. A speculative description of the spectrum is presented for the Sierpinski carpet (SC) where existence, but not uniqueness, of a self-similar Laplacian is known, and also for the octagasket, where even the existence of a self-similar Laplacian is not known. New results about the structure of the spectrum involving "miniaturization" of eigenfunctions are presented.
Statement of Responsibility: by Stacey Goff
Thesis: Thesis (B.A.) -- New College of Florida, 2007
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2007 G6
System ID: NCFE003778:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003778/00001

Material Information

Title: Outer Approximation of the Spectrum of a Fractal Laplacian
Physical Description: Book
Language: English
Creator: Goff, Stacey
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2007
Publication Date: 2007

Subjects

Subjects / Keywords: Fractal
Laplacian
Partial Differential Equations (PDE)
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The Neumann spectrum of a Laplacian on a fractal K in the plane is approximated as a renormalized limit of the Neumann spectra of the standard Laplacian on a sequence of domains which approximate K from the outside. Eigenvalues and eigenfunctions are approximated numerically for lower portions of the spectrum. A speculative description of the spectrum is presented for the Sierpinski carpet (SC) where existence, but not uniqueness, of a self-similar Laplacian is known, and also for the octagasket, where even the existence of a self-similar Laplacian is not known. New results about the structure of the spectrum involving "miniaturization" of eigenfunctions are presented.
Statement of Responsibility: by Stacey Goff
Thesis: Thesis (B.A.) -- New College of Florida, 2007
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2007 G6
System ID: NCFE003778:00001

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