The Resource Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
Resource Information
The item Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a selfcontained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces
 Language
 eng
 Extent
 VIII, 112 p.
 Contents

 Part I: New Structures on Valuations and Applications
 Translation invariant valuations on convex sets
 Valuations on manifolds
 Part II: Algebraic Integral Geometry
 Classical integral geometry
 Curvature measures and the normal cycle
 Integral geometry of euclidean spaces via Alesker theory
 Valuations and integral geometry on isotropic manifolds
 Hermitian integral geometry
 Isbn
 9783034808743
 Label
 Integral Geometry and Valuations
 Title
 Integral Geometry and Valuations
 Statement of responsibility
 by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes
 Language
 eng
 Summary
 Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a selfcontained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces
 http://library.link/vocab/creatorName
 Alesker, Semyon
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Fu, Joseph H.G.
 Gallego, Eduardo.
 Solanes, Gil.
 SpringerLink (Online service)
 Series statement
 Advanced Courses in Mathematics  CRM Barcelona,
 http://library.link/vocab/subjectName

 Mathematics
 Convex geometry
 Discrete geometry
 Differential geometry
 Label
 Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
 Antecedent source
 mixed
 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.
 Contents
 Part I: New Structures on Valuations and Applications  Translation invariant valuations on convex sets  Valuations on manifolds  Part II: Algebraic Integral Geometry  Classical integral geometry  Curvature measures and the normal cycle  Integral geometry of euclidean spaces via Alesker theory  Valuations and integral geometry on isotropic manifolds  Hermitian integral geometry
 Control code
 9783034808743
 Dimensions
 unknown
 Extent
 VIII, 112 p.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783034808743
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783034808743
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)893857980
 Label
 Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)
 Antecedent source
 mixed
 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.
 Contents
 Part I: New Structures on Valuations and Applications  Translation invariant valuations on convex sets  Valuations on manifolds  Part II: Algebraic Integral Geometry  Classical integral geometry  Curvature measures and the normal cycle  Integral geometry of euclidean spaces via Alesker theory  Valuations and integral geometry on isotropic manifolds  Hermitian integral geometry
 Control code
 9783034808743
 Dimensions
 unknown
 Extent
 VIII, 112 p.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783034808743
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783034808743
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)893857980
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/IntegralGeometryandValuationsbySemyon/4s3RKFKWr5k/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/IntegralGeometryandValuationsbySemyon/4s3RKFKWr5k/">Integral Geometry and Valuations, by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>