Integral means and boundary limits of Dirichlet series

@article{Saksman2009IntegralMA,
  title={Integral means and boundary limits of Dirichlet series},
  author={Eero Saksman and Kristian Seip},
  journal={Bulletin of the London Mathematical Society},
  year={2009},
  volume={41}
}
  • E. Saksman, K. Seip
  • Published 4 December 2007
  • Mathematics
  • Bulletin of the London Mathematical Society
This paper deals with the boundary behaviour of functions in the Hardy spaces ℋp for ordinary Dirichlet series. The main result, answering a question of Hedenmalm, shows that the classical Carlson theorem on integral means does not extend to the imaginary axis for functions in ℋ∞ , that is, for the ordinary Dirichlet series in H∞ of the right half‐plane. We discuss an important embedding problem for ℋp , the solution of which is only known when p is an even integer. Viewing ℋp as Hardy spaces… 
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References

SHOWING 1-10 OF 24 REFERENCES
Hardy Spaces of Dirichlet Series and Their Composition Operators
Abstract. In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis
Carleson's convergence theorem for Dirichlet series
A Hilbert space of Dirichlet series is obtained by considering the Dirichlet series f(s) = Sigma(n=1)(infinity) a(n)n(-s) that satisfy Sigma(n=0)(infinity) \a(n)\(2) 1/2 and define a functions tha ...
Dirichlet series and functional analysis
The study of Dirichlet series of the form \( \sum\nolimits_{n = 1}^\infty {a_n n^{ - s} } \) has a long history beginning in the nineteenth century, and the interest was due mainly to the central
Ten lectures on the interface between analytic number theory and harmonic analysis
Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of
Analytic Number Theory
Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large
A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$
For a function $\varphi$ in $L^2(0,1)$, extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates $\varphi(nx)$, $n=1,2,3,\ldots$, constitutes a
MATH
TLDR
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Über die gleichmäßige Konvergenz Dirichletscher Reihen.
Einleitung. Es sei (1.) 0< 1< 2<·. .< <... (lim . = ) n=oo eine Folge reeller Zahlen und (2.) iane-» n=l eine zugehörige Dirichletsche Reihe, die ein Konvergenzgebiet besitzt. Dann existieren
The Legacy of Niels Henrik Abel
The collected works of Niels Henrik Abel, edited by Sophus Lie and Ludwig Sylow in 1881, contain 29 papers. The first was written in 1823 when Abel was 21 years old, and the last was jotted down on
Collected Mathematical Works’, Vol. I, Dirichlet Series and the Riemann Zeta-Function (Danish
  • Mathematical Society,
  • 1952
...
1
2
3
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