Bailleul, Maxime Lefèvre, Pascal

We study some L^p spaces of Dirichlet series, particularly two families of Bergman spaces A^p and B^p. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p=2. We also show that the B^p spaces have properties similar to the classical B...

Sheremeta, Myroslav Mykolayovych Stets, Yulia Vasylivna Sumyk, Oksana Markiyanivna
Published in
Journal of Mathematical Sciences

We study the Dirichlet series with an arbitrary abscissa of absolute convergence. The lower and upper estimates for sums of these series are found. The above results allow us to establish some relations between the maximum modulus and the maximal term of Dirichlet series, especially to find conditions that ensure that the maximum modulus and the ma...

Sowa, Artur
Published in
Functional Analysis and Its Applications

It is observed that the Dirichlet ring admits a representation in an infinite-dimensional matrix algebra. The resulting matrices are subsequently used in the construction of nonorthogonal Riesz bases in a separable Hilbert space. This framework enables custom design of a plethora of bases with interesting features. Remarkably, the representation of...

Zykova, T. V.
Published in
Mathematical Notes

The main result of the paper is the determination of the regularized trace of the Laplace-Beltrami operator with potential on the manifold given by a function family of smooth almost Liouville metrics on the sphere (besides, all the geodesics of these metrics are closed and have equal length).

Laville, Guy

We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.

Delaunay, Christophe Fricain, Emmanuel Mosaki, Elie Robert, Olivier

In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-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 Beurling-Nyman type criterion for the Siegel ...

de Roton, Anne Révész, Szilard

We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold....

Fricain, Emmanuel Delaunay, Christophe Mosaki, Elie Robert, Olivier

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 were described using some spaces of functions which were defined with some technical conditions. Here we give two different natural ways in order to remove those technical conditions. In parti...

Pribitkin, Wladimir de Azevedo

Kayumov, I. R.
Published in
Russian Mathematics

For p ≥ 2 we obtain bounds for Lp-norms of the Fourier transform of real parts of simple partial fractions. For even p our estimate is sharp. We also prove a new inequality for Lp-norms of simple partial fractions which in some cases is stronger than the corresponding inequality obtained by V. Yu. Protasov.