Geodesic
On Differential Operator in Compact Zero-dimensional Groups
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 279-287.

Voir la notice de l'article provenant de la source Math-Net.Ru

We define strong derivative on zero-dimensional compact group and find conditions under which the differential operator does not depend from an orthonormal system that defines this derivative. For multidimensional case we find conditions under which the differential operator does not depend from method of conversion multidimensional group in one-dimensional group. We obtain a clear view of annihilators in a multidimensional compact zero-dimensional group. 
@article{ISU_2014_14_3_a5,
     author = {I. S. Kruss},
     title = {On {Differential} {Operator} in {Compact} {Zero-dimensional} {Groups}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {279--287},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a5/}
}
TY  - JOUR
AU  - I. S. Kruss
TI  - On Differential Operator in Compact Zero-dimensional Groups
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 279
EP  - 287
VL  - 14
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a5/
LA  - ru
ID  - ISU_2014_14_3_a5
ER  - 
%0 Journal Article
%A I. S. Kruss
%T On Differential Operator in Compact Zero-dimensional Groups
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 279-287
%V 14
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a5/
%G ru
%F ISU_2014_14_3_a5
I. S. Kruss. On Differential Operator in Compact Zero-dimensional Groups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 3, pp. 279-287. http://geodesic.mathdoc.fr/item/ISU_2014_14_3_a5/

[1] Butzer P. L., Wagner H. J., “Walsh–Fourier series and the concept of a derivative”, Appl. Anal., 3:1 (1973), 29–46 | DOI | MR | Zbl

[2] Golubov B. I., “A modified strong dyadic integral and derivative”, Sbornik: Mathematics, 193:4 (2002), 507–529 | DOI | DOI | MR | Zbl

[3] Volosivets S. S., “A modified $P$-adic integral and a modified $P$-adic derivative for functions defined on a half-axis”, Russian Math., 49:6 (2005), 25–36 | MR | Zbl

[4] Kozyrev S. V., “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376 | DOI | DOI | MR | Zbl

[5] Lukomskii S. F., “Haar system on a product of zero-dimensional compact group”, Centr. Eur. J. Math., 9:3 (2011), 627–639 | DOI | MR | Zbl

[6] Lukomskii S. F., “Multiresolution analysis on product of zero-dimensional Abelian groups”, J. Math. Anal. Appl., 385 (2012), 1162–1178 | DOI | MR | Zbl

[7] Lukomskii S. F., “Haar series on compact zero-dimmesional abelian group”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 9:1 (2009), 14–19 (in Russian)