# A note on a generalized cohomology equation

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 279-283
- ISSN: 0010-1354

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topKrzyżewski, K.. "A note on a generalized cohomology equation." Colloquium Mathematicae 84/85.2 (2000): 279-283. <http://eudml.org/doc/210813>.

@article{Krzyżewski2000,

abstract = {We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7].},

author = {Krzyżewski, K.},

journal = {Colloquium Mathematicae},

keywords = {cohomology equation; coboundary; ergodic endomorphism},

language = {eng},

number = {2},

pages = {279-283},

title = {A note on a generalized cohomology equation},

url = {http://eudml.org/doc/210813},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Krzyżewski, K.

TI - A note on a generalized cohomology equation

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 279

EP - 283

AB - We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7].

LA - eng

KW - cohomology equation; coboundary; ergodic endomorphism

UR - http://eudml.org/doc/210813

ER -

## References

top- [1] S. Banach et S. Saks, Sur la convergence forte dans les champs ${L}^{p}$, Studia Math. 2 (1930), 51-57. Zbl56.0932.01
- [2] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York, 1958. Zbl0084.10402
- [3] K. Krzyżewski, On regularity of measurable solutions of a cohomology equation, Bull. Polish Acad. Sci. Math. 37 (1989), 279-287. Zbl0762.58022
- [4] K. Krzyżewski, On 4-lacunary sequences generated by ergodic toral endomorphisms, Proc. Amer. Math. Soc. 118 (1993), 469-478. Zbl0783.42016
- [5] K. Krzyżewski, On 4-lacunary sequences generated by some measure preserving maps, Acta Math. Hungar. 74 (1997), 261-278. Zbl0924.28011
- [6] K. Krzyżewski, On some Sidon sequences, Internat. J. Bifurcation Chaos 9 (1999), 1785-1793. Zbl1089.28500
- [7] J. Kwiatkowski, M. Lemańczyk and D. Rudolph, Weak isomorphism of meas- ure-preserving diffeomorphisms, Israel J. Math. 80 (1992), 33-64. Zbl0774.28008
- [8] F. Riesz and B. Sz.-Nagy, Leçons d'Analyse Fonctionnelle, Akadémiai Kiadó, Budapest, 1952.

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