Fixed frequency eigenfunction immersions and supremum norms of random waves
نویسندگان
چکیده
منابع مشابه
On the Supremum of Random Dirichlet Polynomials
logN . One can refer to Bohr [B], Bohnenblust and Hille [BH], Helson [H], Hardy and Riesz [HR], Queffélec [Q3] for this background and related results. This of course, basically justifies the investigation of the supremum of Dirichlet polynomials (see for instance Konyagin and Queffélec [KQ]). The following classical reduction step enables to replace the Dirichlet polynomial by some relevant tr...
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Let D lR N , 0 < (D) < +1 and f : D ! lR is an arbitrary summable function. Then the function F() := R fx2D:f(x)g (f(x) ?) dd (2 lR) is continuous, non-negative, non-increasing, convex, and has almost everywhere the derivative F 0 () = ?f ]. Further on, it holds ess supf = supf 2 lR : F() > 0g, where ess supf denotes the essential supremum of f. These properties can be used for computing esssup...
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ژورنال
عنوان ژورنال: Electronic Research Announcements in Mathematical Sciences
سال: 2015
ISSN: 1935-9179
DOI: 10.3934/era.2015.22.76