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We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f (s) = \sum_{n = 1}^{\infty} a ₙ n^{- s}$ with ${| | f | |}_{\infty} : = s u p_{ℜ s > 0} | f (s) | < \infty$ , then $\sum_{n = 1}^{\infty} | a ₙ | n^{- 2} {\leq | | f | |}_{\infty}$ and even slightly better, and $\sum_{n = 1}^{\infty} | a ₙ | n^{- 1 / 2} {\leq C | | f | |}_{\infty}$ , C being an absolute constant.

The Borel Property for Simple Riesz Means.

Viktor Losert (1986)

Monatshefte für Mathematik

The characterization of series amenable to ratio tests.

A.G. Pakes (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

The class of convolution operators on the Marcinkiewicz spaces

Ka-Sing Lau (1981)

Annales de l'institut Fourier

Let $𝒯_{X}$ denote the operator-norm closure of the class of convolution operators $Φ_{μ} : X \to X$ where $X$ is a suitable function space on $R$ . Let $ℳ_{r}^{p}$ be the closed subspace of regular functions in the Marinkiewicz space $ℳ^{p}$ , $1 \leq p < \infty$ . We show that the space $𝒯_{ℳ_{r}^{p}}$ is isometrically isomorphic to $𝒯_{L^{p}}$ and that strong operator sequential convergence and norm convergence in $𝒯_{ℳ_{r}^{p}}$ coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on $ℳ^{2}$ .

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Tauberian-type theorems with application to the Stieltjes transformation.

Tauber-Sätze und M-Perfektheit.

The Abel-type transformations into $ℓ$ .

The Abel-type transformtions into $G_{w}$ .

The absolute harmonic summability factors of infinite series

The Analysis of k-Step Iterative Methods for Linear Systems from Summability Theory

The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects

The Banach Algebra of Conservative Triangular Matrices.

The Bohr inequality for ordinary Dirichlet series

The Borel Property for Simple Riesz Means.

The characterization of series amenable to ratio tests.

The class of convolution operators on the Marcinkiewicz spaces

The classes of strongly $V_{λ}^{F}$ (A,p)-summable sequences of fuzzy numbers.

The Comparison of Bounded Convergence Domains of Regular Matrices.

The double sequence space $ℓ_{2} (p, f, q, s)$

The dual spaces of the sets of difference sequences of order $m$ .

The fine spectra of some Cesàro generalized operators defined on $ℓ^{p}$ ( $p > 1$ ).

The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.

The general methods of finding the sum $S_{n}$ for all kinds of series, II

The general methods of finding the sum $S_{n}$ for all kinds of series

Currently displaying 21 – 40 of 95