Results 161 to 170 of about 10,947 (207)

Hardy Spaces of Dirichlet Series

2013
The forthcoming spaces \( {{\mathcal{H}}^{p}} \) of Dirichlet series (1 ≤ p ≤ ∞), analogous to the familiar Hardy spaces H p on the unit disk, have been successfully introduced to study completeness problems in Hilbert spaces ([63]), first for p = 2, ∞. Later on, the general case was considered in [10] for the study of composition operators.
Hervé Queffélec, Martine Queffélec
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Discrete observability and dirichlet series

Systems & Control Letters, 1987
The authors consider the problem of recovering the initial data of the heat equation in a bounded domain with standard boundary conditions, by output measurements, discrete in time and space. Using properties of Dirichlet series, they obtain a necessary and sufficient condition of observability.
Gilliam, David S., Martin, Clyde
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On Dirichlet Series with Periodic Coefficients

The Ramanujan Journal, 2002
The author investigates the distribution of zeros of the Dirichlet series \(L(s,f)=\sum_{n=1}^\infty\frac{f(n)}{n^s}\) with \(q\)-periodic coefficients \(f(n)\), i.e. \(f(n+q)=f(n)\) for all integers \(n\) and some fixed integer~\(q\). He finds the zero free regions and, similarly as for the Riemann zeta-function or the Lerch zeta-function, defines ...
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An Inculsion Theorem for Dirichlet Series

Canadian Mathematical Bulletin, 1989
AbstractIt is shown that under certain conditions the asymptotic relationship between two Dirichlet series implies the same relationship with λn replaced by log λn.
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On a certain class of dirichlet series

Applicable Analysis, 1990
Summary: For \(0 < a < 1\) and \(\text{Re} (s) > 1\), let \(L(s,a)\) and \(L^* (s,a)\) be the Dirichlet series \(L(s,a) = \sum^\infty_{n = 1} \cos (2 \pi na) n^{-s}\) and \(L^* (s,a) = \sum_{n = 1 }^\infty \sin (2 \pi na) n^{-s}\). We show that \(L(s,a)\) and \(L^*(s,a)\) have holomorphic extension in the whole complex plane. Values of \(L(s,a)\) and \(
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General Properties of Dirichlet Series

2013
For a real number θ, we denote by ℂ θ the following vertical half-plane: $${\mathbb{C}_\theta } = \left\{ {s \in \mathbb{C};\Re es > \theta } \right\}$$ .
Hervé Queffélec, Martine Queffélec
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Overconvergence Properties of Dirichlet Series

Potential Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Dirichlet Series for Sums of Squares

The Ramanujan Journal, 2003
Let \(L_f(s)=\sum_{n=1}^{\infty }f(n)n^{-s}\) be the generating Dirichlet series of the arithmetic function \(f\). Supposing that \(f_1, f_2, g_1, g_2\) are completely multiplicative, the authors show by multiplicativity arguments that \[ \sum_{n=1}^{\infty }\frac{(f_1*g_1)(n)(f_2*g_2)(n)}{n^s} = \frac{L_{f_1f_2}(s)L_{g_1g_2}(s)L_{f_1g_2}(s)L_{g_1f_2 ...
Borwein, Jonathan Michael, Choi, Kwok-Kwong Stephen   +1 more
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On the growth of an entire dirichlet series

Ukrainian Mathematical Journal, 1999
Summary: We establish a relation between the increase of the quantity \({\mathfrak M}(\sigma,F)=|a_0|+\sum_{n=1}^{\infty}|a_n|\exp(\sigma\lambda_n)\) and the behavior of sequences \(\{|a_n|\}\) and \(\{\lambda_n\}\), where \(\{\lambda_n\}\) is a sequence of nonnegative numbers increasing to \(\infty\), and \(F(s)= a_0+\sum_{n=1}^{\infty}a_n\exp(s ...
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ON THE DERIVATIVE OF AN ENTIRE DIRICHLET SERIES

Mathematics of the USSR-Sbornik, 1990
See the review in Zbl 0656.30001.
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