On Bohr's theorem for general Dirichlet series
Sign Up to like & getrecommendations! Published in 2020 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201800542
Abstract: We present quantitative versions of Bohr's theorem on general Dirichlet series $D=\sum a_{n} e^{-\lambda_{n}s}$ assuming different assumptions on the frequency $\lambda:=(\lambda_{n})$, including the conditions introduced by Bohr and Landau. Therefore using the summation method by… read more here.
Keywords: theorem general; lambda; dirichlet series; bohr theorem ... See more keywords
The differentiation operator in the space of uniformly convergent Dirichlet series
Sign Up to like & getrecommendations! Published in 2020 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201900211
Abstract: Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half‐planes {s∈C|Res>ε} for each ε>0… read more here.
Keywords: differentiation; uniformly convergent; differentiation operator; dirichlet series ... See more keywords
Approximation of analytic functions by an absolutely convergent Dirichlet series
Sign Up to like & getrecommendations! Published in 2021 at "Archiv der Mathematik"
DOI: 10.1007/s00013-021-01616-x
Abstract: In the paper, an absolutely convergent Dirichlet series whose shifts approximate a wide class of analytic functions is constructed. This series is close in the mean to the Riemann zeta-function. read more here.
Keywords: convergent dirichlet; dirichlet series; analytic functions; absolutely convergent ... See more keywords
Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Annalen"
DOI: 10.1007/s00208-016-1511-1
Abstract: 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 multiplicative sequence $$(b_n)$$(bn) of complex numbers is said… read more here.
Keywords: sum; mathscr infty; dirichlet series; holomorphic functions ... See more keywords
The Order of the Dirichlet Series in the Half-Strip
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-019-04455-y
Abstract: We study the Dirichlet series whose domain of convergence is the half-plane, and the sequence of exponents can be extended to a certain “regular” sequence. We prove that the k-orders of the Dirichlet series are… read more here.
Keywords: series half; order dirichlet; series; dirichlet series ... See more keywords
Holomorphic functions of finite order generated by Dirichlet series
Sign Up to like & getrecommendations! Published in 2022 at "Banach Journal of Mathematical Analysis"
DOI: 10.1007/s43037-022-00184-8
Abstract: Given a frequency λ = (λn) and l ≥ 0, we introduce the scale of Banach spaces H ∞,l[Re > 0] of holomorphic functions f on the right half-plane [Re > 0], which satisfy (A)… read more here.
Keywords: riesz; holomorphic functions; order; dirichlet series ... See more keywords
A mean counting function for Dirichlet series and compact composition operators
Sign Up to like & getrecommendations! Published in 2021 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.107775
Abstract: We introduce a mean counting function for Dirichlet series, which plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function does in the classical theory. The… read more here.
Keywords: counting function; mean counting; function; dirichlet series ... See more keywords
Random unconditional convergence of vector-valued Dirichlet series
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2019.06.007
Abstract: We study random unconditionality of Dirichlet series in vector-valued Hardy spaces $\mathcal H_p(X)$. It is shown that a Banach space $X$ has type 2 (respectively, cotype 2) if and only if for every choice $(x_n)_n\subset… read more here.
Keywords: random unconditional; vector valued; unconditional convergence; dirichlet series ... See more keywords
A uniqueness property of general Dirichlet series
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2019.06.007
Abstract: Abstract Let F ( s ) = ∑ n a n / λ n s be a general Dirichlet series which is absolutely convergent on ℜ ( s ) > 1 . Assume that F… read more here.
Keywords: dirichlet series; degree conductor; uniqueness property; general dirichlet ... See more keywords
Formulas for the Riemann zeta-function and certain Dirichlet series
Sign Up to like & getrecommendations! Published in 2018 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2018.1514394
Abstract: ABSTRACT Using known theta identities and formulas of S. Ramanujan and G. Hardy among others we prove several formulas for the Riemann zeta-function and two Dirichlet series. read more here.
Keywords: zeta function; dirichlet series; formulas riemann; riemann zeta ... See more keywords
Linear space properties of $H^p$ spaces of Dirichlet series
Sign Up to like & getrecommendations! Published in 2019 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/7898
Abstract: We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0 read more here.
Keywords: spaces dirichlet; dirichlet series; space properties; linear space ... See more keywords