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Let be a compact subset of a separable Hilbert space with finite fractal dimension , and an orthogonal projection in of rank greater than or equal to . For every , there exists an orthogonal projection in of the same rank as , which is injective when restricted to and such that . This result follows from Mañé’s paper. Thus the inverse of the restricted mapping is well defined. It is natural to ask whether there exists a universal modulus of continuity for the inverse of Mañé’s...
The aim of this work is to establish, from a
mathematical point of view, the limit α → +∞ in the system
where . This corresponds to an approximation
which is made in the context of Langmuir turbulence in plasma
Physics. The L2-subcritical σ (that is σ ≤ 2/3)
and the H1-subcritical σ (that is σ ≤ 2) are
studied. In the physical case σ = 1, the limit is then studied for
the norm.
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