vol13_pp111-121. 174KB Jun 04 2011 12:05:53 AM
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We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field
Proof : The only problem is to prove formula (4), that is to prove that u is the sum of its Taylor expansion with respect to λ. In the case where A is a complex Banach algebra,
In Section 3 we treat the rele- vant deterministic equations and in Section 4 we prove existence, uniqueness and estimates in terms of the data of the solution of the equation
In Section 6 we prove Theorem 3.2 about the convergence of the renormalization branching process to a time-homogeneous limit.. In Section 7 , we prove the statements from
Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as weak Poincaré and weak Cheeger, weighted Poincaré and
We prove the existence of a sphere of unoccupied plaquettes enclosing the origin (rather than just a sphere intersecting no occupied bond), and we do so for all dimensions..
Using Talagrand’s abstract concentration inequality in product spaces and the related kernel method for empirical processes [14] we will first prove a general result that
We prove that for almost all values of the index α – except for a dense set of Lebesgue measure zero – the asymptotic series which were obtained in [13] are in fact
