A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$

@article{Hedenmalm1995AHS,
  title={A Hilbert space of Dirichlet series and systems of dilated functions in \$L^2(0,1)\$},
  author={H̊akan Hedenmalm and Peter Lindqvist and Kristian Seip},
  journal={Duke Mathematical Journal},
  year={1995},
  volume={86},
  pages={1-37}
}
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 Riesz basis or a complete sequence in $L^2(0,1)$. The problem translates into a question concerning multipliers and cyclic vectors in the Hilbert space $\cal H$ of Dirichlet series $f(s)=\sum_n a_nn^{-s}$, where the coefficients $a_n$ are square summable. It proves useful to model $\cal H$ as the $H… 
Zeros of functions in Hilbert spaces of Dirichlet series
The Dirichlet–Hardy space $${\fancyscript{H}}^2$$ consists of those Dirichlet series $$\sum _n a_n n^{-s}$$ for which $$\sum _n |a_n|^2<\infty $$. It is shown that the Blaschke condition in the
Hardy–Orlicz Spaces of Dirichlet Series: An Interpolation Problem on Abscissae of Convergence
The study of Hardy spaces of Dirichlet series denoted by $\mathscr{H}^p$ ($p\geq 1$) was initiated in [7] when $p=2$ and $p=\infty $, and in [2] for the general case. In this paper we introduce the
Riesz means in Hardy spaces on Dirichlet groups
Given a frequency $$\lambda =(\lambda _n)$$ λ = ( λ n ) , we study when almost all vertical limits of a $$\mathcal {H}_1$$ H 1 -Dirichlet series $$\sum a_n e^{-\lambda _ns}$$ ∑ a n e - λ n s are
Zeros of Functions in Bergman-Type Hilbert Spaces of Dirichlet Series
For a real number $\alpha$ the Hilbert space $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha 0$. Generalizations
Hardy spaces of vector-valued Dirichlet series
Given a Banach space $X$ and $1 \leq p \leq \infty$, it is well known that the two Hardy spaces $H_p(\mathbb{T},X)$ ($\mathbb{T}$ the torus) and $H_p(\mathbb{D},X)$ ($\mathbb{D}$ the disk) have to be
Composition Operators on Bohr-Bergman Spaces of Dirichlet Series
For $\alpha \in \mathbb{R}$, let $\mathscr{D}_\alpha$ denote the scale of Hilbert spaces consisting of Dirichlet series $f(s) = \sum_{n=1}^\infty a_n n^{-s}$ that satisfy $\sum_{n=1}^\infty
Fréchet spaces of general Dirichlet series
Inspired by a recent article on Frechet spaces of ordinary Dirichlet series $\sum a_n n^{-s}$ due to J.~Bonet, we study topological and geometrical properties of certain scales of Frechet spaces of
Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables
Let $${\mathscr {H}}_\infty $$H∞ be the set of all ordinary Dirichlet series $$D=\sum _n a_n n^{-s}$$D=∑nann-s representing bounded holomorphic functions on the right half plane. A completely
Hardy spaces of general Dirichlet series — a survey
The main purpose of this article is to survey on some key elements of a recent $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$, which was mainly inspired by the work
Extending Landau's Theorem on Dirichlet Series with Non-Negative Coefficients
A classical theorem of Landau states that, if an ordinary Dirichlet series has non-negative coefficients, then it has a singularity on the real line at its abscissae of absolute convergence. In this
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 21 REFERENCES
Foundations of the theory of Dirichlet series
1. A modern reader, familiar with the methods of functional analysis, is struck with the conviction tha t the classical theory of Dirichlet series [3, 5, 6] must have content expressible in more
An introduction to nonharmonic Fourier series
Bases in Banach Spaces - Schauder Bases Schauder's Basis for C[a,b] Orthonormal Bases in Hilbert Space The Reproducing Kernel Complete Sequences The Coefficient Functionals Duality Riesz Bases The
An Introduction to the Theory of Numbers
This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,
On the convergence of multiple Fourier series
Inequality (1) follows from the special case in which P is a triangle with a vertex at the origin; for any polygon breaks up into triangles, and the characteristic function of any triangle is a
What is ergodic theory
Ergodic theory involves the study of transformations on measure spaces. Interchanging the words “measurable function” and “probability density function” translates many results from real analysis to
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
Theory of Probability
TLDR
This chapter discusses random events and their Probabilities, the theory of Stochastic Processes, and the properties of Random Valuables and Distribution Functions.
Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe
[Aus dem dreizehnten Bande der Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen.]
Compact groups and dirichlet series
Representing Measures and Hardy Spaces for the Infinite Polydisk Algebra
...
1
2
3
...