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Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 372, Issue 9, pp. 6677 - 6702
We study H^p spaces of Dirichlet series, called \mathcal {H}^p, for the range 0 MATHEMATICS | HARDY-SPACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2018, Volume 465, Issue 2, pp. 839 - 856
We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically... 
Abscissa | Dirichlet series | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | APPROXIMATION | HARDY-SPACES | CONVERGENCE
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 08/2019, Volume 277, Issue 3, pp. 786 - 805
We initiate the study of interpolation of the Hardy spaces of Dirichlet series. We prove that there are no variants of the classical interpolation theorems in... 
Interpolation spaces | Dirichlet series | Interpolation functor | Hardy spaces | Computer science
Journal Article
JOURNAL OF FUNCTIONAL ANALYSIS, ISSN 0022-1236, 03/2015, Volume 268, Issue 6, pp. 1612 - 1648
By a theorem of Gordon and Hedenmalm, phi generates a bounded composition operator on the Hilbert space H-2 of Dirichlet series Sigma(n) b(n)n(-s) with... 
INTERPOLATION | MATHEMATICS | Hardy space H-2 | Approximation numbers | COMPACT COMPOSITION OPERATORS | BOUNDED ANALYTIC FUNCTIONS | Composition operators | HILBERT-SPACE | Decay rates
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 12/2016, Volume 86, Issue 4, pp. 453 - 473
Let $${\mathscr{H}^2}$$ H 2 denote the space of ordinary Dirichlet series with square summable coefficients, and let $${\mathscr{H}^{2}_{0}}$$ H 0 2 denote its... 
Square function | Secondary 30B50 | Analysis | Hankel form | Mathematics | Dirichlet series | Primary 47B35 | Weak product space | MATHEMATICS | HARDY-SPACES | HILBERT-SPACE | POLYNOMIALLY BOUNDED OPERATORS | SUMS | Mathematics - Functional Analysis | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Mathematische Annalen, ISSN 0025-5831, 06/2017, Volume 368, Issue 1-2, pp. 837 - 876
Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A... 
46E50 | 30B50 | 42B30 | 46G25 | POLYNOMIALS | MATHEMATICS | HARDY-SPACES | CONVERGENCE | POLYDISK | INEQUALITY | Mathematics - Functional Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2015, Volume 426, Issue 1, pp. 340 - 363
We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases,... 
Weighted Bergman spaces | Dirichlet series | Carleson measure | Essential norm | Generalized Nevanlinna counting function | Composition operator | MATHEMATICS | MATHEMATICS, APPLIED | HARDY-SPACES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 01/2020, Volume 278, Issue 2, p. 108320
We consider composition operators Cφ on the Hardy space of Dirichlet series H2, generated by Dirichlet series symbols φ. We prove two different subordination... 
Dirichlet series | Composition operator | Hardy space
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2639 - 2653
We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy... 
46B07 | 30B50 | Theoretical, Mathematical and Computational Physics | Abscissas of convergence | Mathematics, general | Mathematics | Dirichlet series | Applications of Mathematics | Hardy space | MATHEMATICS | Dirichlet problem | Mathematics - Functional Analysis
Journal Article
ANNALES DE L INSTITUT FOURIER, ISSN 0373-0956, 2016, Volume 66, Issue 2, pp. 551 - 588
By a theorem of the first named author, phi generates a bounded composition operator on the Hardy space H-p of Dirichlet series (1 <= p < infinity) only if... 
Dirichlets series | MATHEMATICS | composition operators | BANACH-SPACES | HARDY-SPACES | POLYDISK | approximation numbes
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 06/2017, Volume 220, Issue 2, pp. 509 - 530
We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s, u) = Sigma a(n)n(-s-(u) over bar), and characterize when such a... 
ARVESON-HARDY SPACE | INTERPOLATION | MATHEMATICS | HILBERT-SPACES | ALGEBRAS | BESOV-SOBOLEV SPACES | THEOREM | Hilbert space | Research | Mathematical research | Series, Dirichlet
Journal Article
Studia Mathematica, ISSN 0039-3223, 2015, Volume 226, Issue 1, pp. 17 - 55
The Hardy spaces of Dirichlet series, denoted by H-p (p >= 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general... 
Riemann zeta function | Dirichlet series | Bergman spaces | Hardy spaces | MATHEMATICS | HILBERT-SPACES | COMPOSITION OPERATORS | Riemann zeta | function | HARDY-SPACES | COEFFICIENTS
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2019, Volume 25, Issue 6, pp. 3220 - 3258
Inspired by results of Bayart on ordinary Dirichlet series $$\sum a_n n^{-s}$$ ∑ a n n - s , the main purpose of this article is to start an $${\mathcal... 
30B50 | Hardy spaces | Mathematics | General Dirichlet series | Bohr compactification | Secondary 30H10 | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | Approximations and Expansions | Primary 43A17 | Partial Differential Equations
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 03/2015, Volume 268, Issue 6, pp. 1612 - 1648
By a theorem of Gordon and Hedenmalm, φ generates a bounded composition operator on the Hilbert space H2 of Dirichlet series ∑nbnn−s with square-summable... 
Composition operators | Approximation numbers | Hardy space [formula omitted] | Decay rates | Hardy space H
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2013, Volume 365, Issue 6, pp. 3227 - 3253
-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a... 
Dirichlet series | Beurling-nyman criterion | Zeros of L-functions | Hardy spaces | MATHEMATICS | HYPOTHESIS | RIEMANN ZETA-FUNCTION | Beurling-Nyman criterion | zeros of L-functions | SUMS | Functional Analysis | Mathematics | Number Theory
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2016, Volume 41, Issue 1, pp. 129 - 142
For alpha is an element of R, let D-alpha, denote the scale of Hilbert spaces consisting of Dirichlet series f(s) = Sigma(infinity)(n=1) a(n)n(-s) that satisfy... 
Composition operators | Dirichlet series | Bergman spaces | MATHEMATICS | THEOREM | HANKEL FORMS | HARDY | Mathematics - Functional Analysis
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 261, Issue 9, pp. 2669 - 2696
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet... 
Carleson measures | Dirichlet series | Hardy space in infinitely many complex variables | MATHEMATICS | COMPOSITION OPERATORS | PRODUCT BMO | FRAMES | THEOREM | HARDY-SPACES | VARIABLES | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2013, Volume 273, Issue 3, pp. 999 - 1023
In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions... 
Beurling–Nyman criterion | Pascal matrix | Hardy spaces | 11M26 | Mathematics, general | Mathematics | Dirichlet series | Zeros of L -functions | 30H10 | Beurling-Nyman criterion | Zeros of L-functions | MATHEMATICS | Functional Analysis | Number Theory
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 2/2018, Volume 90, Issue 1, pp. 1 - 12
By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $$\mathcal {H}^2$$ H2 , the space of Dirichlet series... 
47B38 | Secondary: 11M36 | 37C30 | Analysis | Schur test | Composition operator | Zeta function | Mathematics | Dirichlet series | Primary: 47B33 | Hardy space | MATHEMATICS | SERIES | HILBERT-SPACE | H-2
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 6/2009, Volume 41, Issue 3, pp. 411 - 422
This paper deals with the boundary behaviour of functions in the Hardy spaces p for ordinary Dirichlet series. The main result, answering a question of... 
MATHEMATICS | HARDY-SPACES
Journal Article
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