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1.

図書
図書
1. An introduction to the geometrical analysis of vector fields : with applications to maximum principles and Lie groups
Stefano Biagi, Andrea Bonfiglioli
出版情報: New Jersey : World Scientific, c2019  xxv, 423 p. ; 25 cm
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目次情報: 続きを見る
Preface
Flows of Vector Fields in Space / 1：
Notations for vector fields in space / 1.1：
The flow of a vector field / 1.2：
The semigroup property / 1.2.1：
Global vector fields / 1.2.2：
Regular and singular points / 1.2.3：
Differentiation along a flow / 1.3：
The equation of variation for the flow / 1.4：
A Liouville Theorem for ODEs / 1.4.1：
Further regularity of the flow / 1.4.2：
Flowing through X, Y, -X, -Y: commutators / 1.5：
The product of exponentials: motivations / 1.6：
Exercises / 1.7：
The Exponential Theorem / 2：
Main algebraic setting / 2.1：
The Exponential Theorem for K [t] / 2.2：
Two crucial lemmas of non-commutative algebra / 2.2.1：
Poincare's ODE in the formal power series setting / 2.2.2：
The Exponential Theorem for K<> / 2.3：
Dynkin's Formula / 2.4：
A Dynkin-type formula / 2.4.1：
Dynkin's original formula / 2.4.2：
Identities from the Exponential Theorem / 2.5：
The Exponential Theorem for K [s, t] / 2.6：
The algebra K<(x, y> [s, t] / 2.6.1：
The Exponential Theorem for K[s, t] / 2.6.2：
Poincaré's PDEs on K [s, t] / 2.6.3：
More identities / 2.7：
Appendix: manipulations of formal series / 2.8：
The Composition of Flows of Vector Fields / 2.9：
Again on commutators / 3.1：
Composition of flows of vector fields / 3.2：
Approximation for higher order commutators / 3.3：
Appendix: another identity between formal power series / 3.4：
Hadamard's Theorem for Flows / 3.5：
Preliminaries on derivations and differentials / 4.1：
Time-dependent vector fields / 4.1.1：
Relatedness of vector fields and flows / 4.2：
Invariance of a vector field under a map / 4.2.1：
Commutators and Lie-derivatives / 4.3：
Hadamard's Theorem for flows / 4.4：
Commuting vector fields / 4.5：
Hadamard's Theorem for flows in space / 4.6：
Series expansibility / 4.6.1：
Conjugation of flows / 4.6.2：
The CBHD Operation on Finite Dimensional Lie Algebras / 4.7：
Local convergence of the CBHD series / 5.1：
Recursive identities for Dynkin's polynomials / 5.2：
Poincaré's ODE on Lie algebras / 5.3：
More Poincare-type ODEs / 5.3.1：
The local associativity of the CBHD series / 5.4：
Appendix: multiple series in Banach spaces / 5.5：
The Connectivity Theorem / 5.6：
Hörmander systems of vector fields / 6.1：
A useful Linear Algebra lemma / 6.2：
X-subunit curves and X-connectedness / 6.3：
Connectivity for Hörmander vector fields / 6.3.2：
The Carnot-Carathéodory distance / 6.4：
The X-control distance / 7.1：
Some equivalent definitions of d-x / 7.2：
Basic topological properties of the CC-distance / 7.3：
Euclidean boundedness of the dx balls / 7.3.1：
Length space property / 7.3.2：
The Weak Maximum Principle / 7.4：
Main definitions / 8.1：
Picone's Weak Maximum Principle / 8.2：
Existence of L-barriers / 8.3：
The parabolic Weak Maximum Principle / 8.4：
Appendix: semiellipticity and the WMP / 8.5：
Corollaries of the Weak Maximum Principle / 8.6：
Comparison principles / 9.1：
Maximum-modulus and Maximum Principle / 9.2：
The parabolic case / 9.2.1：
An a priori estimate / 9.3：
Application: Green and Poisson operators / 9.4：
Appendix: Another Maximum Principle / 9.5：
The Maximum Propagation Principle / 9.6：
Assumptions on the operators / 10.1：
Principal vector fields / 10.2：
Propagation and Strong Maximum Principle / 10.3：
Invariant sets and the Nagumo-Bony Theorem / 10.4：
The Hopf Lemma / 10.5：
The proof of the Propagation Principle / 10.6：
Conclusions and a résumé / 10.6.1：
The Maximum Propagation along the Drift / 10.7：
Propagation along the drift / 11.1：
A résumé of drift propagation / 11.2：
The point of view of reachable sets / 11.3：
Examples of propagation sets for a PDO / 11.3.1：
The Differential of the Flow wrt its Parameters / 11.4：
The non-autonomous equation of variation / 12.1：
The autonomous equation of variation / 12.1.1：
More on flow differentiation / 12.2：
Appendix: A review of linear ODEs / 12.3：
The Exponential Theorem for ODEs / 12.4：
Finite-dimensional algebras of vector fields / 13.1：
The differential of the flow wrt the vector held / 13.2：
The Exponential Theorem for Lie Groups / 13.3：
The differential of the Exponential Map / 14.1：
The Exponential Theorem for Lie groups / 14.2：
An alternative approach with analytic functions / 14.3：
The Local Third Theorem of Lie / 14.4：
Local Lie's Third Theorem / 15.1：
Global Lie's Third Theorem in the nilpotent case / 15.2：
The Exponential Map of G / 15.2.1：
Construction of Carnot Groups / 15.3：
Finite-dimensional stratified Lie algebras / 16.1：
Construction of Carnot groups / 16.2：
Exponentiation of Vector Field Algebras into Lie Groups / 16.3：
The assumptions for the exponentiation / 17.1：
Construction of the local Lie group / 17.2：
The local Lie-group multiplication / 17.2.1：
The local left invariance of g / 17.2.2：
Local to global / 17.3：
Schur's ODE on g and prolongation of solutions / 17.3.1：
On the Convergence of the CBHD Series / 17.4：
A domain of convergence for the CBHD series / 18.1：
Some prerequisites of Linear Algebra / 18.2：
Algebras and Lie algebras / A.1：
Stratified Lie algebras / A.1.1：
Positive semidefinite matrices / A.2：
The Moore-Penrose pseudo-inverse / A.3：
Dependence Theory for ODEs / A.4：
Review of basic ODE Theory / B.1：
Preliminaries / B.1.1：
Maximal solutions / B.1.2：
ODEs depending on parameters / B.1.3：
Continuous dependence / B.2：
The Arzelà-Ascoli Theorem / B.2.1：
Dependence on the equation / B.2.2：
Dependence on the datum / B.2.3：
Dependence on the parameters / B.2.4：
Ck dependence / B.3：
The equation of variation / B.3.1：
C¿ dependence / B.4：
A brief review of Lie Group Theory / B.5：
A short review of Lie groups / C.1：
The Lie algebra of G / C.1.1：
The exponential map of G / C.1.2：
Right invariant vector fields / C.1.3：
Lie's First Theorem / C.1.4：
Homomorphisms / C.2：
A few examples / C.3：
Further Readings / C.4：
List of abbreviations
Bibliography
Index
Preface
Flows of Vector Fields in Space / 1：
Notations for vector fields in space / 1.1：
2.

図書
図書
2. Lie groups, Lie algebras, and some of their applications
Robert Gilmore
出版情報: New York : Wiley, c1974  xx, 587 p. ; 23 cm
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3.

図書
図書
3. Lectures on Lie groups (: pbk ; : cloth)
[by] J. Frank Adams
出版情報: New York : W.A. Benjamin, 1969  xii, 182 p. ; 23 cm
シリーズ名: Mathematics lecture note series
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4.

図書
図書
4. Elliptic operators and compact groups (: Germany ; : U.S.)
Michael Francis Atiyah
出版情報: Berlin ; New York : Springer-Verlag, 1974  93 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 401
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5.

図書
図書
5. Abelian harmonic analysis, theta functions and function algebras on a nilmanifold (: Germany ; : U.S.)
Louis Auslander, Richard Tolimieri
出版情報: Berlin ; New York : Springer-Verlag, 1975  98 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 436
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6.

図書
図書
6. Lie groups and Lie algebras (pt. 1: chapters 1-3 : us ; pt. 1: chapters 1-3 : fr)
Nicolas Bourbaki
出版情報: Paris : Hermann , Reading, Mass. : Addison-Wesley, c1975-  v. ; 24 cm
シリーズ名: Actualités scientifiques et industrielles ; . Elements of mathematics
Adiwes international series in mathematics
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7.

図書
図書
7. Real reductive groups (v. 1 ; v. 2)
Nolan R. Wallach
出版情報: Boston ; Tokyo : Academic Press, c1988-c1992  2 v. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 132, 132-2
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8.

図書
図書
8. Introduction to compact transformation groups
Glen E. Bredon
出版情報: New York : Academic Press, 1972  xiii, 459 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; v. 46
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9.

図書
図書
9. Hardy spaces on homogeneous groups (pbk.)
by G.B. Folland and E.M. Stein
出版情報: Princeton, N.J. : Princeton University Press , [Tokyo] : University of Tokyo Press, 1982  284 p. ; 24 cm
シリーズ名: Mathematical notes ; 28
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10.

図書
図書
10. Quantum statistical mechanics and Lie group harmonic analysis (Pt. A)
Norman Hurt and Robert Hermann
出版情報: Brookline, MA : Math Sci Press, [1980]-  v. <1 > ; 24 cm
シリーズ名: Lie groups : history, frontiers, and applications ; Vol. 10
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