| Title:
|
The Perron product integral in Lie groups (English) |
| Author:
|
Morales, Pedro |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
43 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
349-366 |
| . |
| Category:
|
math |
| . |
| MSC:
|
22E30 |
| MSC:
|
26A39 |
| MSC:
|
28B10 |
| idZBL:
|
Zbl 0811.28008 |
| idMR:
|
MR1211757 |
| DOI:
|
10.21136/CMJ.1993.128392 |
| . |
| Date available:
|
2009-09-24T09:30:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128392 |
| . |
| Reference:
|
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| Reference:
|
[2] W. M. Boothby: An introduction to differentiable manifolds and Riemannian geometry.Second Edition, Academic Press, New York, 1986. Zbl 0596.53001, MR 0861409 |
| Reference:
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[3] N. Bourbaki: Variétes différentielles et analytiques.Fascicule de résultats, Diffusion CCLS, Paris, 1982. |
| Reference:
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[4] N. Bourbaki: Groupes et algèbres de Lie.Chapitres 2 et 3, Diffusion CCLS, Paris, 1982. Zbl 0505.22006 |
| Reference:
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[5] J. D. Dollard, C. N. Friedman: Product Integration with Applications to Differential Equations.Addison-Wesley Publishing Company, Reading, Massachusetts, 1979. MR 0552941 |
| Reference:
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[6] J.-F. Hamilton: Multiplicative Riemann integration and logarithmic differentiation in Lie algebras and Lie groups.Doctoral dissertation, Indiana University, 1973. |
| Reference:
|
[7] M. Hausner, J. T. Schwartz: Lie Groups; Lie Algebras.Gordon and Breach, Science Publishers, Inc., Great Britain, 1968. MR 0235065 |
| Reference:
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[8] R. Henstock: Lectures on the Theory of Integration.World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
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[9] R. Henstock: General Theory of Integration.Clarendon Press, Oxford, 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
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[10] J. Jarník, J. Kurzweil: A general form of the product integral and linear ordinary differential equations.Czechoslovak Math. J. 37 (1987), 642–659. MR 0913996 |
| Reference:
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[11] K. Kuratowski: Topology I.Academic Press, London, 1966. MR 0217751 |
| Reference:
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[12] J. Kurzweil: Nichtabsolut konvergente Integrale.Teubner-Texte zur Mathematik no 26, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
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[13] R. M. McLeod: The generalized Riemann integral.Carus Mathematical Monographs no 20, Mathematical Association of America, 1980. Zbl 0486.26005, MR 0588510 |
| Reference:
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[14] Y. Matsuchima: Differentiable Manifolds.Marcel Dekker, Inc., New York, 1972. MR 0346831 |
| Reference:
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[15] D. Montgomery, L. Zippin: Topological Transformation Groups.Interscience Publishers, New York, 1955. MR 0073104 |
| Reference:
|
[16] P. Morales: Product integral for finite-dimensional Lie algebra-valued functions.Proc. Workshop on Functional Integration with emphasis on the Feynman Integral, Sherbrooke, Québec, Canada 1986, Suppl. Rend. Circ. Mat. Palermo 17 (1987), 313–329. MR 0950422 |
| Reference:
|
[17] G. Rasch: Zur Theorie und Anwendung des Produktintegrals.J. Reine Angew. Math. 191 (1934), 65–119. Zbl 0009.16503 |
| Reference:
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[18] L. Schlesinger: Neue Grundlagen für einen Infinitesimalkalkül der Matrizen.Math. Z. 33 (1931), 33–61. 10.1007/BF01174342 |
| Reference:
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[19] L. Schlesinger: Weitere Beiträge zum Infinitesimalkalkül der Matrizen.Math. Z. 35 (1932), 485–501. Zbl 0004.24701, MR 1545305, 10.1007/BF01186565 |
| Reference:
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[20] V. S. Varadarajan: Lie Groups, Lie Algebras and their Representations.Prentice-Hall, Inc., New Jersey, 1974. Zbl 0371.22001, MR 0376938 |
| Reference:
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[21] V. Volterra: Sulla teoria delle equazioni differenziali lineari.Rend. Circ. Mat. Palermo 2 (1888), 69–75. 10.1007/BF03018073 |
| Reference:
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[22] V. Volterra, B. Hostinsky: Opérations infinitésimales linéaires.Gauthier-Villars, Paris, 1938. |
| Reference:
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[23] F. W. Warner: Foundations of Differentiable Manifold and Lie groups.Springer-Verlag, New York, 1983. MR 0722297 |
| . |
