The Resource Analysis on Lie Groups with Polynomial Growth, by Nick Dungey, A.F.M. (Tom) ter Elst, Derek William Robinson, (electronic resource)

Analysis on Lie Groups with Polynomial Growth, by Nick Dungey, A.F.M. (Tom) ter Elst, Derek William Robinson, (electronic resource)

Label
Analysis on Lie Groups with Polynomial Growth
Title
Analysis on Lie Groups with Polynomial Growth
Statement of responsibility
by Nick Dungey, A.F.M. (Tom) ter Elst, Derek William Robinson
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one. This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory
Member of
http://library.link/vocab/creatorName
Dungey, Nick
Dewey number
512/.55
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • xect1ggBMjA
  • 55HUgwbXnzw
  • CnewlgRos-k
Image bit depth
0
Language note
English
LC call number
  • QA252.3
  • QA387
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • ter Elst, A.F.M. (Tom).
  • Robinson, Derek William.
Series statement
Progress in Mathematics,
Series volume
214
http://library.link/vocab/subjectName
  • Topological Groups
  • Global analysis
  • Operator theory
  • Topological Groups, Lie Groups
  • Global Analysis and Analysis on Manifolds
  • Operator Theory
Label
Analysis on Lie Groups with Polynomial Growth, by Nick Dungey, A.F.M. (Tom) ter Elst, Derek William Robinson, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
I Introduction -- II General Formalism -- II.1 Lie groups and Lie algebras -- II.2 Subelliptic operators -- II.3 Subelliptic kernels -- II.4 Growth properties -- II.5 Real operators -- II.6 Local bounds on kernels -- II.7 Compact groups -- II.8 Transference method -- II.9 Nilpotent groups -- II.10 De Giorgi estimates -- II.11 Almost periodic functions -- II.12 Interpolation -- Notes and Remarks -- III Structure Theory -- III.1 Complementary subspaces -- III.2 The nilshadow; algebraic structure -- III.3 Uniqueness of the nilshadow -- III.4 Near-nilpotent ideals -- III.5 Stratified nilshadow -- III.6 Twisted products -- III.7 The nilshadow; analytic structure -- Notes and Remarks -- IV Homogenization and Kernel Bounds -- IV.1 Subelliptic operators -- IV.2 Scaling -- IV.3 Homogenization; correctors -- IV.4 Homogenized operators -- IV.5 Homogenization; convergence -- IV.6 Kernel bounds; stratified nilshadow -- IV.7 Kernel bounds; general case -- Notes and Remarks -- V Global Derivatives -- V.1 L2-bounds -- V.2 Gaussian bounds -- V.3 Anomalous behaviour -- Notes and Remarks -- VI Asymptotics -- VI. 1 Asymptotics of semigroups -- VI.2 Asymptotics of derivatives -- Notes and Remarks -- Appendices -- A.1 De Giorgi estimates -- A.2 Morrey and Campanato spaces -- A.3 Proof of Theorem II.10.5 -- A.4 Rellich lemma -- Notes and Remarks -- References -- Index of Notation
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (VIII, 312 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220626
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-2062-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089820
  • (SSID)ssj0000805103
  • (PQKBManifestationID)11458001
  • (PQKBTitleCode)TC0000805103
  • (PQKBWorkID)10835439
  • (PQKB)10138240
  • (DE-He213)978-1-4612-2062-6
  • (MiAaPQ)EBC3075709
  • (EXLCZ)993400000000089820
Label
Analysis on Lie Groups with Polynomial Growth, by Nick Dungey, A.F.M. (Tom) ter Elst, Derek William Robinson, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
I Introduction -- II General Formalism -- II.1 Lie groups and Lie algebras -- II.2 Subelliptic operators -- II.3 Subelliptic kernels -- II.4 Growth properties -- II.5 Real operators -- II.6 Local bounds on kernels -- II.7 Compact groups -- II.8 Transference method -- II.9 Nilpotent groups -- II.10 De Giorgi estimates -- II.11 Almost periodic functions -- II.12 Interpolation -- Notes and Remarks -- III Structure Theory -- III.1 Complementary subspaces -- III.2 The nilshadow; algebraic structure -- III.3 Uniqueness of the nilshadow -- III.4 Near-nilpotent ideals -- III.5 Stratified nilshadow -- III.6 Twisted products -- III.7 The nilshadow; analytic structure -- Notes and Remarks -- IV Homogenization and Kernel Bounds -- IV.1 Subelliptic operators -- IV.2 Scaling -- IV.3 Homogenization; correctors -- IV.4 Homogenized operators -- IV.5 Homogenization; convergence -- IV.6 Kernel bounds; stratified nilshadow -- IV.7 Kernel bounds; general case -- Notes and Remarks -- V Global Derivatives -- V.1 L2-bounds -- V.2 Gaussian bounds -- V.3 Anomalous behaviour -- Notes and Remarks -- VI Asymptotics -- VI. 1 Asymptotics of semigroups -- VI.2 Asymptotics of derivatives -- Notes and Remarks -- Appendices -- A.1 De Giorgi estimates -- A.2 Morrey and Campanato spaces -- A.3 Proof of Theorem II.10.5 -- A.4 Rellich lemma -- Notes and Remarks -- References -- Index of Notation
Dimensions
unknown
Edition
1st ed. 2003.
Extent
1 online resource (VIII, 312 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461220626
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-1-4612-2062-6
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089820
  • (SSID)ssj0000805103
  • (PQKBManifestationID)11458001
  • (PQKBTitleCode)TC0000805103
  • (PQKBWorkID)10835439
  • (PQKB)10138240
  • (DE-He213)978-1-4612-2062-6
  • (MiAaPQ)EBC3075709
  • (EXLCZ)993400000000089820

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