| Title:
|
Bochner product integration (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
305-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2]. (English) |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
Bochner integral |
| Keyword:
|
product integral |
| Keyword:
|
Bochner product integral |
| MSC:
|
26A42 |
| MSC:
|
28B05 |
| idZBL:
|
Zbl 0830.28006 |
| idMR:
|
MR1305532 |
| DOI:
|
10.21136/MB.1994.126162 |
| . |
| Date available:
|
2009-09-24T21:06:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126162 |
| . |
| Reference:
|
[1] J. D. Dollard C.N. Friedman: Product Integration with Applications to Differential Equations.Addison-Wesley Publ. Company, Reading, Massachusetts, 1979. MR 0552941 |
| Reference:
|
[2] J. D. Dollard C.N. Friedman: On strong product integration.J. Func. Anal. 28 (1978), 309-354. MR 0492656, 10.1016/0022-1236(78)90091-5 |
| Reference:
|
[3] N. Dunford J.T. Schwartz: Linear Operators I..Interscience Publishers, New York, London, 1958. MR 0117523 |
| Reference:
|
[4] R. D. Gill S. Johansen: A survey of product-integration with a view toward application in survival analysis.Annals of Statistics 18 (1990), no. 4, 1501-1555. MR 1074422, 10.1214/aos/1176347865 |
| Reference:
|
[5] R. Henstock: Lectures on the Theory of Integration.World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[6] R. Henstock: The General Theory of Integration.Clarendon Press, Oxfoгd, 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[7] E. Hille R. S. Phillips: Functional Analysis and Semi-groups.American Mathematical Society, Providence, 1957. MR 0089373 |
| Reference:
|
[8] J. Jarník J. Kurzweil: Perron integral, Perron product integral and ordinary linear differential equations.EQUADIFF 6, Lecture Notes in Mathematics 1192, Springer, Berlin (1986), 149-154. MR 0877117 |
| Reference:
|
[9] J. Jarník J. Kurzweil: A general form of the product integral and linear ordinary differential equations.Czech. Math. Јournal 37 (1987), 642-659. MR 0913996 |
| Reference:
|
[10] J. Kurzweil: Nichtabsolut konvergente Integrale.BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[11] J. Mawhin: Analyse. Fondements,techniques,évolution.De Boeck-Wesmael, Bruxelles, 1992. Zbl 0759.26004, MR 1190926 |
| Reference:
|
[12] E. J. McShane: Unified Integration.Academic Press, New York, London, 1983. Zbl 0551.28001, MR 0740710 |
| Reference:
|
[13] L. Schlesinger: Vorlesungen über lineare Differentialgleichungen.Teubner, Leipzig, 1908. |
| Reference:
|
[14] L. Schlesinger: Neue Grundlagen für einen Infinitesimalkalkul der Matrizen.Math. Zeitschrift 33 (1931), 33-61. Zbl 0001.01503, 10.1007/BF01174342 |
| Reference:
|
[15] G. Schmidt: On multiplicative Lebesgue integration and families of evolution operators.Math. Scand. 29 (1971), 113-133. Zbl 0232.47024, MR 0352398, 10.7146/math.scand.a-11039 |
| Reference:
|
[16] Š. Schwabik: The Perron product integral and generalized linear differential equations.Časopis pěst. mat. 115 (1990), 368-404. Zbl 0724.26006, MR 1090861 |
| Reference:
|
[17] Š. Schwabik: Generalized Ordinary Differential Equations.World Scientific, Singapore, 1992. Zbl 0781.34003, MR 1200241 |
| Reference:
|
[18] V. Volterra: Sulle equazioni differenziali lineari.Rend. Accademia dei Lincei 3 (1887), 393-396. |
| Reference:
|
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| Reference:
|
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| . |
