Majorant series for the<i>N</i>-body problem

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 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 ...

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

Special Quadrature Error Estimates and Their Application in the Hardy-littlewood Majorant Problem

The Hardy-Littlewood majorant problem has a positive answer only for exponents p which are even integers, while there are counterexamples for all p / ∈ 2N. Montgomery conjectured that there exist counterexamples even among idempotent polynomials. This was proved recently by Mockenhaupt and Schlag with some four-term idempotents. However, Mockenhaupt conjectured that even the classical 1 + e ± e...