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1.
A. A. Abilov 《Mathematical Notes》1992,52(1):631-635
Let
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2.
Florin P. Boca Alexandru Zaharescu 《Transactions of the American Mathematical Society》2006,358(4):1797-1825
Let denote the repartition of the -level correlation measure of the finite set of directions , where is the fixed point and is an integer lattice point in the square . We show that the average of the pair correlation repartition over in a fixed disc converges as . More precisely we prove, for every and , the estimate
We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence. 3.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
,
4.
Pavel Drábek 《Annali di Matematica Pura ed Applicata》1991,159(1):1-16
We consider the nonlinear Dirichlet boundary value problems for the second order equation
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