On the Hardy–Littlewood majorant problem for arithmetic sets

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

On the Hardy–Littlewood Majorant Problem

Let Λ ⊆ {1, . . . , N}, and let {an}n∈Λ be a sequence with |an| ≤ 1 for all n. It is easy to see that ∥∥∥∥ ∑ n∈Λ ane(nθ) ∥∥∥∥ p ≤ ∥∥∥∥ ∑ n∈Λ e(nθ) ∥∥∥∥ p for every even integer p. We give an example which shows that this statement can fail rather dramatically when p is not an even integer. This answers in the negative a question known as the Hardy-Littlewood majorant conjecture, thereby ruling ...

A Majorant Problem

Let f(z) akzk a 0 be analytlc in the unlt disc. Any k=O o Inflnlte complex vector e (eo,et,e2 ) such that lekl 1, k 0,1,2 induces a function re(Z) akekZk whlch is still analytic k=O In the unit disc. In this paper we study the problem of maximizing the p-means: over all possible vectors e and for values of r close to 0 and for all p<2. k It is proved that a maxlmlzlng function Is f,{z} -laoi + ...

On the Hardy - Littlewood majorant

Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets

It has been known for more than thirty years that the degree of a non-standard model of true arithmetic is a subuniform upper bound for the arithmetic sets (suub). Here a notion of generic enumeration is presented with the property that the degree of such an enumeration is an suub but not the degree of a non-standard model of true arithmetic. This anwers a question posed in the literature.