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
Resource Information
The item Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (viii, 880 pages)
- 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
- 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
- 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
- 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
- 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
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Topics-in-geometric-analysis-and-harmonic/y36peW2C7A0/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Topics-in-geometric-analysis-and-harmonic/y36peW2C7A0/">Topics in geometric analysis and harmonic analysis on spaces of homogeneous type, by Ryan Alvarado</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
