Geodesic
On results of Jan Mařík in the theory of derivatives
Mathematica Bohemica, Tome 121 (1996) no. 4, pp. 385-395

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
Results of Jan Marik on the theory of derivatives of real functions are described.
Results of Jan Marik on the theory of derivatives of real functions are described.
DOI : 10.21136/MB.1996.126042
Classification : 01A70, 26A24
Keywords: derivative; multiplier 
Zajíček, Luděk. On results of Jan Mařík in the theory of derivatives. Mathematica Bohemica, Tome 121 (1996) no. 4, pp. 385-395. doi: 10.21136/MB.1996.126042
@article{10_21136_MB_1996_126042,
     author = {Zaj{\'\i}\v{c}ek, Lud\v{e}k},
     title = {On results of {Jan} {Ma\v{r}{\'\i}k} in the theory of derivatives},
     journal = {Mathematica Bohemica},
     pages = {385--395},
     year = {1996},
     volume = {121},
     number = {4},
     doi = {10.21136/MB.1996.126042},
     mrnumber = {1428141},
     zbl = {0879.01027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126042/}
}
TY  - JOUR
AU  - Zajíček, Luděk
TI  - On results of Jan Mařík in the theory of derivatives
JO  - Mathematica Bohemica
PY  - 1996
SP  - 385
EP  - 395
VL  - 121
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126042/
DO  - 10.21136/MB.1996.126042
LA  - en
ID  - 10_21136_MB_1996_126042
ER  - 
%0 Journal Article
%A Zajíček, Luděk
%T On results of Jan Mařík in the theory of derivatives
%J Mathematica Bohemica
%D 1996
%P 385-395
%V 121
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126042/
%R 10.21136/MB.1996.126042
%G en
%F 10_21136_MB_1996_126042

[Br1] A. Bruckner: Density preserving homeomorphisms and a theorem of Maximoff. Quart. J. Math. Oxford 21 (1970), 337-347. | DOI | MR | Zbl

[Br2] A. Bruckner: Differentiation of real functions. 2nd ed. CRM monograph series; vol. 5, Providence, 1994. | MR | Zbl

[Bu] Z. Buczolich: Second Peano derivatives are not extendable. Real Anal. Exchange 14 (1988/89), 423-428. | DOI | MR

[BW] Z. Buczolich C. E. Weil: Extending Peano Differentiable Functions. Preprint. | MR

[CT] G. E. Cross B. S. Thomson: Symmetric integrals and trigonometric series. Dissertationes Math. 319 (1992). | MR

[F1] R. Fleissner: Multiplication and the fundamental theorem of calculus: A survey. Real Anal. Exchange 2 (1976), 7-34. | MR

[F2] R. Fleissner: Distant bounded variation and products of derivatives. Fund. Math. XCIV (1977), 1-11. | MR | Zbl

[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

[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).

[LP] M. Laczkovich G. Petruska: On the transformers of derivatives. Fund. Math. 100 (1978), 179-199. | DOI | MR

[Mal] A. Maliszewski: Characteristic functions and products of bounded derivatives. Proc. Amer. Math. Soc. 123 (1995), 2203-2211. | DOI | MR | Zbl

[M1] J. Mařík: Generalized integrals and trigonometric series. Unpublished manuscript.

[M2] J. Mařík: On generalized derivatives. Real Anal. Exchange 3 (1977/78), 87-92.

[M3] S. J. Agronsky R. Biskner. A. M. Bruckner, J. Mařík: Representations of functions by derivatives. Trans. Amer. Math. Soc. 263 (1981), 493-500. | DOI | MR

[M4] J. Mařík: On a space of functions representable by derivatives. Real Anal. Exchange 7 (1981/82), 135-148. | DOI | MR

[M5] J. Mařík: Multipliers of summable derivatives. Real Anal. Exchange 8 (1982/83), 486-493. | DOI | MR

[M6] J. Mařík: Some properties of multipliers of summable derivatives. Real Anal. Exchange 9 (1983/84), 251-257. | DOI | MR

[M7] J. Mařík: Multipliers of nonnegative derivatives. Real Anal. Exchange 9 (1983/84), 258-272. | DOI | MR

[M8] J. Mařík, C. E. Weil: Products of powers of nonnegative derivatives. Trans. Amer. Math. Soc 276 (1983), 361-373. | DOI | MR

[M9] J. Mařík: Derivatives and closed sets. Acta Math. Hungar. 43 (1984), 25-29. | DOI | MR

[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

[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

[M12] J. Mařík: Characteristic functions and products of derivatives. Real Anal. Exchange 16 (1990/91), 245-254. | DOI | MR

[M13] J. Mařík, C E. Weil: Sums of powers of derivatives. Proc Amer. Math. Soc. 112 (1991), 807-817. | DOI | MR

[M14] J. Mařík: Derivatives and convexity. Real Anal. Exchange 17 (1991/92), 745-747. | MR

[M15] A. M. Bruckner J. Mařík, C. E. Weil: Some aspects of products of derivatives. Amer. Math. Monthly 99 (1992), 134-145. | DOI | MR

[M16] J. Mařík: Derivatives, continuous functions and bounded Lebesgue functions. Real Anal. Exchange 18 (1992/93), 169-175. | MR

[M17] J. Mařík: Norms and derivatives. Real Anal. Exchange 18 (1992/93), 343-351. | MR

[M18] H. Fejzic J. Mařík, C. E. Weil: Extending Peano derivatives. Math. Bohem. 119 (1994), 387-406. | MR

[M19] J. Mařík: Generalized derivatives. Real Anal. Exchange 5 (1979/80), 315-317.

[Max] I. Maximoff: Sur la transformation continue de quelques fonctions en derivées exactes. Bull. Soc. Phys. Math. Kazan (3) 12 (1940), 57-81. | MR | Zbl

[P1] D. Preiss: Level sets of derivatives. Trans. Amer. Math. Soc. 272 (1982), 161-184. | DOI | MR | Zbl

[P2] D. Preiss: Algebra generated by derivatives. Real Anal. Exchange 8 (1982/83), 208-216. | MR

[P3] D. Preiss: Maximoff's theorem. Real Anal. Exchange 5 (1979/80), 92-104. | MR

[T] B. S. Thomson: Symmetric properties of real functions. M. Dekker, New York, 1994. | MR | Zbl

[Z] Z. Zahorski: Sur la première dérivée. Trans. Amer. Math. Soc. 69 (1950), 1-54. | MR | Zbl

Cité par Sources :