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The Resource Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado

Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado

Label
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
Title
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
Statement of responsibility
by Ryan Alvarado
Creator
Contributor
Author
Thesis advisor
Subject
Genre
Language
eng
Summary
The present dissertation consists of three main parts. One theme underscoring the work carried out in this dissertation concerns the relationship between analysis and geometry. As a first illustration of the interplay between these two branches of mathematics we develop a sharp theory of Hardy spaces in the setting of spaces of homogeneous type. The presented work is in collaboration with M. Mitrea. In the second part, we prove that a function defined on a subset of a geometrically doubling quasi-metric space which satisfies a Holder-type condition may be extended to the entire space with preservation of regularity. The proof proceeds along the lines of the original work of Whitney in 1934 and yields a linear extension operator. A similar extension result is also proved in the absence of the geometrically doubling hypothesis, albeit the resulting extension procedure is nonlinear in this case. This work is done in collaboration I. Mitrea and M. Mitrea. In the final part of the dissertation we prove that an open, proper, nonempty subset of R n is a locally Lyapunov domain if and only if it satisfies a uniform hour-glass condition. Additionally, we prove a sharp generalization of the Hopf-Oleinik boundary point principle for domains satisfying a one-sided, interior pseudo-ball condition, for semi-elliptic operators with singular drift. These results have been obtained in collaboration with D. Brigham, V. Mazya, M. Mitrea, and E. Ziadþe
Cataloging source
MUU
http://library.link/vocab/creatorName
Alvarado, Ryan
Degree
PhD
Dissertation note
Thesis
Dissertation year
2015.
Government publication
government publication of a state province territory dependency etc
Granting institution
University of Missouri--Columbia
Illustrations
illustrations
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
  • theses
http://library.link/vocab/relatedWorkOrContributorName
Mitrea, Marius
http://library.link/vocab/subjectName
  • Geometric analysis
  • Harmonic analysis
  • Spaces of homogeneous type
Label
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado
Instantiates
Publication
Note
  • Abstract from short.pdf file
  • "A Dissertation presented to the Faculty of the Graduate School at the University of Missouri In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy."
  • Dissertation supervisor: Dr. Marius Mitrea
  • Includes vita
Bibliography note
Includes bibliographical references (pages 859-879)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
958080643
Extent
1 online resource (viii, 880 pages)
Form of item
online
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
Specific material designation
remote
System control number
(OCoLC)958080643
Label
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado
Publication
Note
  • Abstract from short.pdf file
  • "A Dissertation presented to the Faculty of the Graduate School at the University of Missouri In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy."
  • Dissertation supervisor: Dr. Marius Mitrea
  • Includes vita
Bibliography note
Includes bibliographical references (pages 859-879)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
958080643
Extent
1 online resource (viii, 880 pages)
Form of item
online
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
Specific material designation
remote
System control number
(OCoLC)958080643

Library Locations

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      1020 Lowry Street, Columbia, MO, 65201, US
      38.944491 -92.326012
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