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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Ergodic Solenoidal Homology II:
Density of Ergodic Solenoids
Author(s):
Vicente Muñoz and Ricardo Pérez Marco
Instituto de Ciencias Matem
áticas CSIC-UAM-UC3M-UCM,Abstract:
A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy. A measured solenoid immersed in a smooth manifold produces a closed current (known as a generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (up to scalars) transversal measure. It is known that for any smooth manifold, any real homology class is represented by a uniquely ergodic solenoid. In this paper, we prove that the currents associated to uniquely ergodic solenoids are dense in the space of closed currents, therefore proving the abundance of such objects.
Paper's Title:
Invariant Subspaces Close to Almost Invariant Subspaces for Bounded Linear Operators
Author(s):
M. A. Farzaneh, A. Assadi and H. M. Mohammadinejad
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: farzaneh@birjand.ac.ir
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: assadi-aman@birjand.ac.ir
Department of Mathematical and
Statistical Sciences,
University of Birjand,
PO Box 97175/615, Birjand,
Iran.
E-mail: hmohammadin@birjand.ac.ir
Abstract:
In this paper, we consider some features of almost invariant subspace notion. At first, we restate the notion of almost invariant subspace and obtain some results. Then we try to achieve an invariant subspace completely close to an almost invariant subspace. Also, we introduce the notion of "almost equivalent subspaces" to simply the subject related to almost invariant subspaces and apply it.
Paper's Title:
Euler-Maclaurin Formulas for Functions of Bounded Variation
Author(s):
G. De Marco, M. De Zotti, C. Mariconda
Dipartimento di Matematica Tullio Levi-Civita,
Universita degli Studi di Padova
Via Trieste 63, Padova 35121,
Italy.
E-mail: carlo.mariconda@unipd.it
URL: http://www.math.unipd.it
Abstract:
The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on R. We formulate here the analogue for functions that are just of bounded variation.
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