Hardy-Bennett-type theorems

Binary Additive Problems: Theorems of Landau and Hardy-littlewood Type

We prove theorems of Landau and Hardy-Littlewood type for Goldbach, Chen, Lemoime-Levy and other binary partitions of positive integers. We also pose some new conjectures.

Hardy-Littlewood Theorems for A-Harmonic Tensors

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise...

Disproofs of Bell, GHZ, and Hardy Type Theorems and the Illusion of Entanglement

An elementary topological error in Bell’s representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among th...

Comparison theorems of Kolmogorov type and exact values of n-widths on Hardy-Sobolev classes

Let Sβ := {z ∈ C : |Imz| < β} be a strip in complex plane. H̃r ∞,β denotes those 2π-periodic, real-valued functions on R which are analytic in the strip Sβ and satisfy the condition |f (r)(z)| ≤ 1, z ∈ Sβ . Osipenko and Wilderotter obtained the exact values of the Kolmogorov, linear, Gel′fand, and information n-widths of H̃r ∞,β in L∞[0, 2π], r = 0, 1, 2, . . ., and 2n-widths of H̃r ∞,β in Lq [0, ...