Title:
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On results of Jan Mařík in the theory of derivatives (English) |
Author:
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Zajíček, Luděk |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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121 |
Issue:
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4 |
Year:
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1996 |
Pages:
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385-395 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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Results of Jan Marik on the theory of derivatives of real functions are described. (English) |
Keyword:
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derivative |
Keyword:
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multiplier |
MSC:
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01A70 |
MSC:
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26A24 |
idZBL:
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Zbl 0879.01027 |
idMR:
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MR1428141 |
DOI:
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10.21136/MB.1996.126042 |
. |
Date available:
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2009-09-24T21:21:18Z |
Last updated:
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2020-07-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/126042 |
. |
Reference:
|
[Br1] A. Bruckner: Density preserving homeomorphisms and a theorem of Maximoff.Quart. J. Math. Oxford 21 (1970), 337-347. Zbl 0196.07701, MR 0268333, 10.1093/qmath/21.3.337 |
Reference:
|
[Br2] A. Bruckner: Differentiation of real functions.2nd ed. CRM monograph series; vol. 5, Providence, 1994. Zbl 0796.26004, MR 1274044 |
Reference:
|
[Bu] Z. Buczolich: Second Peano derivatives are not extendable.Real Anal. Exchange 14 (1988/89), 423-428. MR 0995982, 10.2307/44151957 |
Reference:
|
[BW] Z. Buczolich C. E. Weil: Extending Peano Differentiable Functions.Preprint. MR 1428765 |
Reference:
|
[CT] G. E. Cross B. S. Thomson: Symmetric integrals and trigonometric series.Dissertationes Math. 319 (1992). MR 1171794 |
Reference:
|
[F1] R. Fleissner: Multiplication and the fundamental theorem of calculus: A survey.Real Anal. Exchange 2 (1976), 7-34. MR 0507383 |
Reference:
|
[F2] R. Fleissner: Distant bounded variation and products of derivatives.Fund. Math. XCIV (1977), 1-11. Zbl 0347.26009, MR 0425041 |
Reference:
|
[Ch] G. Choquet: Application des propriétés descriptives de la fonction contingent a la théorie des fonctions de variable réelle et a la géometrie différentielle des variétés cartésiennes.(Thesis). J. Math. Pures Appl. 26 (1947), 115-256. MR 0023897 |
Reference:
|
[J] V. Jarník: Sur l'extension du domaine de definition des fonctions d'une variable, qui laisse intacte la derivabilité de la fonction.Bull. international de l'Acad. Sci. de Bohême (1923). |
Reference:
|
[LP] M. Laczkovich G. Petruska: On the transformers of derivatives.Fund. Math. 100 (1978), 179-199. MR 0509545, 10.4064/fm-100-3-179-199 |
Reference:
|
[Mal] A. Maliszewski: Characteristic functions and products of bounded derivatives.Proc. Amer. Math. Soc. 123 (1995), 2203-2211. Zbl 0833.26008, MR 1246531, 10.1090/S0002-9939-1995-1246531-4 |
Reference:
|
[M1] J. Mařík: Generalized integrals and trigonometric series.Unpublished manuscript. |
Reference:
|
[M2] J. Mařík: On generalized derivatives.Real Anal. Exchange 3 (1977/78), 87-92. |
Reference:
|
[M3] S. J. Agronsky R. Biskner. A. M. Bruckner, J. Mařík: Representations of functions by derivatives.Trans. Amer. Math. Soc. 263 (1981), 493-500. MR 0594421, 10.1090/S0002-9947-1981-0594421-7 |
Reference:
|
[M4] J. Mařík: On a space of functions representable by derivatives.Real Anal. Exchange 7 (1981/82), 135-148. MR 0646645, 10.2307/44153398 |
Reference:
|
[M5] J. Mařík: Multipliers of summable derivatives.Real Anal. Exchange 8 (1982/83), 486-493. MR 0700199, 10.2307/44153420 |
Reference:
|
[M6] J. Mařík: Some properties of multipliers of summable derivatives.Real Anal. Exchange 9 (1983/84), 251-257. MR 0742788, 10.2307/44153531 |
Reference:
|
[M7] J. Mařík: Multipliers of nonnegative derivatives.Real Anal. Exchange 9 (1983/84), 258-272. MR 0742789, 10.2307/44153532 |
Reference:
|
[M8] J. Mařík, C. E. Weil: Products of powers of nonnegative derivatives.Trans. Amer. Math. Soc 276 (1983), 361-373. MR 0684515, 10.2307/1999439 |
Reference:
|
[M9] J. Mařík: Derivatives and closed sets.Acta Math. Hungar. 43 (1984), 25-29. MR 0731958, 10.1007/BF01951320 |
Reference:
|
[M10] J. Mařík: Transformation and multiplication of derivatives.Classical real analysis (Madison, Wis., 1982). Contemp. Math. 42, Amer. Math. Soc, Providence, R.I., 1985, pp. 119-134. MR 0807985 |
Reference:
|
[M11] A. M. Bruckner J. Mařík, C. E. Weil: Baire one, null functions.Classical real analysis (Madison, Wis., 1982). Contemp. Math. 42, Amer. Math. Soc, Providence, R.I., 1985, pp. 29-41. MR 0807974 |
Reference:
|
[M12] J. Mařík: Characteristic functions and products of derivatives.Real Anal. Exchange 16 (1990/91), 245-254. MR 1087488, 10.2307/44153693 |
Reference:
|
[M13] J. Mařík, C E. Weil: Sums of powers of derivatives.Proc Amer. Math. Soc. 112 (1991), 807-817. MR 1042268, 10.2307/2048705 |
Reference:
|
[M14] J. Mařík: Derivatives and convexity.Real Anal. Exchange 17 (1991/92), 745-747. MR 1171413 |
Reference:
|
[M15] A. M. Bruckner J. Mařík, C. E. Weil: Some aspects of products of derivatives.Amer. Math. Monthly 99 (1992), 134-145. MR 1144354, 10.1080/00029890.1992.11995823 |
Reference:
|
[M16] J. Mařík: Derivatives, continuous functions and bounded Lebesgue functions.Real Anal. Exchange 18 (1992/93), 169-175. MR 1205509 |
Reference:
|
[M17] J. Mařík: Norms and derivatives.Real Anal. Exchange 18 (1992/93), 343-351. MR 1228400 |
Reference:
|
[M18] H. Fejzic J. Mařík, C. E. Weil: Extending Peano derivatives.Math. Bohem. 119 (1994), 387-406. MR 1316592 |
Reference:
|
[M19] J. Mařík: Generalized derivatives.Real Anal. Exchange 5 (1979/80), 315-317. |
Reference:
|
[Max] I. Maximoff: Sur la transformation continue de quelques fonctions en derivées exactes.Bull. Soc. Phys. Math. Kazan (3) 12 (1940), 57-81. Zbl 0063.03850, MR 0015456 |
Reference:
|
[P1] D. Preiss: Level sets of derivatives.Trans. Amer. Math. Soc. 272 (1982), 161-184. Zbl 0508.26001, MR 0656484, 10.1090/S0002-9947-1982-0656484-0 |
Reference:
|
[P2] D. Preiss: Algebra generated by derivatives.Real Anal. Exchange 8 (1982/83), 208-216. MR 0694508 |
Reference:
|
[P3] D. Preiss: Maximoff's theorem.Real Anal. Exchange 5 (1979/80), 92-104. MR 0557966 |
Reference:
|
[T] B. S. Thomson: Symmetric properties of real functions.M. Dekker, New York, 1994. Zbl 0809.26001, MR 1289417 |
Reference:
|
[Z] Z. Zahorski: Sur la première dérivée.Trans. Amer. Math. Soc. 69 (1950), 1-54. Zbl 0038.20602, MR 0037338 |
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