The Resource Weakly analytic vectorvalued measures, by Annela Rämmer Kelly
Weakly analytic vectorvalued measures, by Annela Rämmer Kelly
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The item Weakly analytic vectorvalued measures, by Annela Rämmer Kelly 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 2 library branches.
Resource Information
The item Weakly analytic vectorvalued measures, by Annela Rämmer Kelly 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 2 library branches.
 Summary
 The research for my dissertation focuses on studying vectorvalued measures that are weakly analytic and scalarvalued measures that are Rieszanalytic. My research stems from a wellknown result in harmonic analysis; the celebrated F. and M. Riesz theorem. The main result of the dissertation generalizes an extension of this result for vectorvalued measures. For scalarvalued measures, the classical F. and M. Riesz theorem states that if $\mu,$ a Borel measure defined on the unit circle T, is analytic, then $\mu$ is absolutely continuous with respect to Lebesgue measure m. There are several extensions to this theorem. Lately, Asmar and MontgomerySmith generalized the conclusion that $\mu$ translates continuously for measures on locally compact Hausdorff spaces. They proved that under certain conditions on T, where $T=\{T\sb{t}\}\sb{t\in R}$ is a collection of uniformly bounded invertible isomorphisms of the space of measures, whenever the measure $\mu$ is weakly analytic, then the mapping $t\to T\sb{t}\mu$ is continuous. We will prove a similar result for vectorvalued measures. More precisely, let $\Sigma$ be the $\sigma$algebra of subsets of a set $\Omega$ and $Y\sp{\*}$ be the dual of a Banach space Y. We will assume that $Y\sp{\*}$ has the ARNP and consider vectorvalued measures taking values in $Y\sp{\*}.$ Let $T=\{T\sb{t}\}\sb{t\in R}$ be a collection of uniformly bounded invertible isomorphisms of this space of measures. A vectorvalued measure $\mu$ with values in $Y\sp{\*}$ is called weakly analytic if $\forall A\in\Sigma,\ \forall y\in Y,$ the mapping $t\to x(T\sb{t}\mu(A))\in H\sp{\infty}(\IR).$ In the dissertation we will show that if a measure $\mu$ is weakly analytic, then under certain conditions on $T,\ t\to T\sb{t}\mu$ is absolutely continuous. Let us return to the scalarvalued measures again. DeLeeuw and Glicksberg generalized the F. and M. Riesz theorem, they showed that if a Borel measure on a compact abelian group G is $\varphi$analytic, then the measure is quasiinvariant. We will follow their footsteps and show that if $\mu$ is RieszEanalytic and $E\subset\ G$ satisfies certain conditions, then $\mu$ is quasiinvariant
 Language
 eng
 Label
 Weakly analytic vectorvalued measures
 Title
 Weakly analytic vectorvalued measures
 Statement of responsibility
 by Annela Rämmer Kelly
 Language
 eng
 Summary
 The research for my dissertation focuses on studying vectorvalued measures that are weakly analytic and scalarvalued measures that are Rieszanalytic. My research stems from a wellknown result in harmonic analysis; the celebrated F. and M. Riesz theorem. The main result of the dissertation generalizes an extension of this result for vectorvalued measures. For scalarvalued measures, the classical F. and M. Riesz theorem states that if $\mu,$ a Borel measure defined on the unit circle T, is analytic, then $\mu$ is absolutely continuous with respect to Lebesgue measure m. There are several extensions to this theorem. Lately, Asmar and MontgomerySmith generalized the conclusion that $\mu$ translates continuously for measures on locally compact Hausdorff spaces. They proved that under certain conditions on T, where $T=\{T\sb{t}\}\sb{t\in R}$ is a collection of uniformly bounded invertible isomorphisms of the space of measures, whenever the measure $\mu$ is weakly analytic, then the mapping $t\to T\sb{t}\mu$ is continuous. We will prove a similar result for vectorvalued measures. More precisely, let $\Sigma$ be the $\sigma$algebra of subsets of a set $\Omega$ and $Y\sp{\*}$ be the dual of a Banach space Y. We will assume that $Y\sp{\*}$ has the ARNP and consider vectorvalued measures taking values in $Y\sp{\*}.$ Let $T=\{T\sb{t}\}\sb{t\in R}$ be a collection of uniformly bounded invertible isomorphisms of this space of measures. A vectorvalued measure $\mu$ with values in $Y\sp{\*}$ is called weakly analytic if $\forall A\in\Sigma,\ \forall y\in Y,$ the mapping $t\to x(T\sb{t}\mu(A))\in H\sp{\infty}(\IR).$ In the dissertation we will show that if a measure $\mu$ is weakly analytic, then under certain conditions on $T,\ t\to T\sb{t}\mu$ is absolutely continuous. Let us return to the scalarvalued measures again. DeLeeuw and Glicksberg generalized the F. and M. Riesz theorem, they showed that if a Borel measure on a compact abelian group G is $\varphi$analytic, then the measure is quasiinvariant. We will follow their footsteps and show that if $\mu$ is RieszEanalytic and $E\subset\ G$ satisfies certain conditions, then $\mu$ is quasiinvariant
 Additional physical form
 Also available on the Internet.
 Cataloging source
 MUU
 http://library.link/vocab/creatorDate
 1967
 http://library.link/vocab/creatorName
 Kelly, Annela Rämmer
 Degree
 Ph. D.
 Dissertation year
 1996.
 Government publication
 government publication of a state province territory dependency etc
 Granting institution
 University of MissouriColumbia
 Index
 no index present
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/subjectName

 Vectorvalued measures
 Riesz spaces
 Hausdorff measures
 Target audience
 specialized
 Label
 Weakly analytic vectorvalued measures, by Annela Rämmer Kelly
 Note

 Typescript
 Vita
 Bibliography note
 Includes bibliographical references (leaves 6061)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 38597354
 Dimensions
 29 cm
 Extent
 v, 62 leaves
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Specific material designation
 remote
 Label
 Weakly analytic vectorvalued measures, by Annela Rämmer Kelly
 Note

 Typescript
 Vita
 Bibliography note
 Includes bibliographical references (leaves 6061)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Control code
 38597354
 Dimensions
 29 cm
 Extent
 v, 62 leaves
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/WeaklyanalyticvectorvaluedmeasuresbyAnnela/easRUhvceOU/" 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/WeaklyanalyticvectorvaluedmeasuresbyAnnela/easRUhvceOU/">Weakly analytic vectorvalued measures, by Annela Rämmer Kelly</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>