Erratum for “Generalized dirichlet series and $B$-functions”

Ben Lichtin

Displaying similar documents to “Erratum for “Generalized dirichlet series and $B$ -functions””

Admissible functions for the Dirichlet space

Javad Mashreghi, Mahmood Shabankhah (2010)

Studia Mathematica

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Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of $^{\infty}$ .

On unitary equivalence of invariant subspaces of the Dirichlet space

Kunyu Guo, Liankuo Zhao (2010)

Studia Mathematica

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It is shown that in the Dirichlet space , two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift $M_{z}$ are unitarily equivalent only if ℳ ₁ = ℳ ₂.

On the Dirichlet problem associated with the Dunkl Laplacian

Mohamed Ben Chrouda (2016)

Annales Polonici Mathematici

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This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian $Δ_{k}$ as well as the hypoellipticity of $Δ_{k}$ on noninvariant open sets.

On the Dirichlet problem in the Cegrell classes

Rafał Czyż, Per Åhag (2004)

Annales Polonici Mathematici

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Let μ be a non-negative measure with finite mass given by $φ (d d^{c} ψ) ⁿ$ , where ψ is a bounded plurisubharmonic function with zero boundary values and $φ \in L^{q} ((d d^{c} ψ) ⁿ)$ , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.

On Dirichlet type spaces on the unit ball of $ℂ^{n}$

Małgorzata Michalska (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we discuss characterizations of Dirichlet type spaces on the unit ball of $ℂ^{n}$ obtained by P. Hu and W. Zhang [2], and S. Li [4].

The Dirichlet-Bohr radius

Daniel Carando, Andreas Defant, Domingo A. Garcí, Manuel Maestre, Pablo Sevilla-Peris (2015)

Acta Arithmetica

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Denote by Ω(n) the number of prime divisors of n ∈ ℕ (counted with multiplicities). For x∈ ℕ define the Dirichlet-Bohr radius L(x) to be the best r > 0 such that for every finite Dirichlet polynomial $\sum_{n \leq x} a_{n} n^{- s}$ we have $\sum_{n \leq x} | a_{n} | r^{Ω (n)} \leq s u p_{t \in ℝ} | \sum_{n \leq x} a_{n} n^{- i t} |$ . We prove that the asymptotically correct order of L(x) is ${(l o g x)}^{1 / 4} x^{- 1 / 8}$ . Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows translating various results...

On zeros of Dirichlet’s $L$ -functions.

Н.Г. Чудаков ([unknown])

Matematiceskij sbornik

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IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products

Sophie Grivaux (2013)

Studia Mathematica

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If ${(n_{k})}_{k \geq 1}$ is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle is said to be IP-Dirichlet with respect to ${(n_{k})}_{k \geq 1}$ if $σ ̂ (\sum_{k \in F} n_{k}) \to 1$ as F runs over all non-empty finite subsets F of ℕ and the minimum of F tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz...

Envelope of Dirichlet problems on a domain in $C^{n}$

Eric Bedford (1985)

Annales Polonici Mathematici

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Laplace type operators: Dirichlet problem

Wojciech Kozł (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into $𝖲𝖮 (n)$ -irreducible subspaces.

The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, H. Queffélec (2006)

Studia Mathematica

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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.

Dirichlet forms on quotients of shift spaces

Manfred Denker, Atsushi Imai, Susanne Koch (2007)

Colloquium Mathematicae

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We define thin equivalence relations ∼ on shift spaces $^{\infty}$ and derive Dirichlet forms on the quotient space $Σ =^{\infty} / \sim$ in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.

Estimates of eigenvalues and eigenfunctions in periodic homogenization

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen (2013)

Journal of the European Mathematical Society

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For a family of elliptic operators with rapidly oscillating periodic coefficients, we study the convergence rates for Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The results rely on an $O (ϵ)$ estimate in $H^{1}$ for solutions with Dirichlet condition.

Wiener's type regularity criteria on the complex plane

Józef Siciak (1997)

Annales Polonici Mathematici

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We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that $d (t^{- 1} E \cap | z - a | \leq 1) \geq c o n s t > 0$ for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is...

Discrete Green's function and maximum principles

Vejchodský, Tomáš, Šolín, Pavel

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In this paper the discrete Green’s function (DGF) is introduced and its fundamental properties are proven. Further it is indicated how to use these results to prove the discrete maximum principle for 1D Poisson equation discretized by the $h p$ -FEM with pure Dirichlet or with mixed Dirichlet-Neumann boundary conditions and with piecewise constant coefficient.

The mean value of |L(k,χ)|² at positive rational integers k ≥ 1

Stéphane Louboutin (2001)

Colloquium Mathematicae

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Let k ≥ 1 denote any positive rational integer. We give formulae for the sums $S_{o d d} (k, f) = \sum_{χ (- 1) = - 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 odd Dirichlet characters modulo f > 2) whenever k ≥ 1 is odd, and for the sums $S_{e v e n} (k, f) = \sum_{χ (- 1) = + 1} | L (k, χ) | ²$ (where χ ranges over the ϕ(f)/2 even Dirichlet characters modulo f>2) whenever k ≥ 1 is even.

Normality criteria and multiple values II

Yan Xu, Jianming Chang (2011)

Annales Polonici Mathematici

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Let ℱ be a family of meromorphic functions defined in a domain D, let ψ (≢ 0, ∞) be a meromorphic function in D, and k be a positive integer. If, for every f ∈ ℱ and z ∈ D, (1) f≠ 0, $f^{(k)} \neq 0$ ; (2) all zeros of $f^{(k)} - ψ$ have multiplicities at least (k+2)/k; (3) all poles of ψ have multiplicities at most k, then ℱ is normal in D.

The comparison principle and Dirichlet problem in the class $_{p} (f)$ , p > 0

Pham Hoang Hiep (2006)

Annales Polonici Mathematici

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We establish the comparison principle in the class $_{p} (f)$ . The result obtained is applied to the Dirichlet problem in $_{p} (f)$ .

Normal families and shared values of meromorphic functions

Mingliang Fang, Lawrence Zalcman (2003)

Annales Polonici Mathematici

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Let ℱ be a family of meromorphic functions on a plane domain D, all of whose zeros are of multiplicity at least k ≥ 2. Let a, b, c, and d be complex numbers such that d ≠ b,0 and c ≠ a. If, for each f ∈ ℱ, $f (z) = a \Leftrightarrow f^{(k)} (z) = b$ , and $f^{(k)} (z) = d \Rightarrow f (z) = c$ , then ℱ is a normal family on D. The same result holds for k=1 so long as b≠(m+1)d, m=1,2,....

Essential norms of weighted composition operators on the space $ℋ^{\infty}$ of Dirichlet series

Pascal Lefèvre (2009)

Studia Mathematica

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We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space $ℋ^{\infty}$ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

The Dirichlet problem with sublinear nonlinearities

Aleksandra Orpel (2002)

Annales Polonici Mathematici

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We investigate the existence of solutions of the Dirichlet problem for the differential inclusion $0 \in Δ x (y) + \partial_{x} G (y, x (y))$ for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional $J (x) = \int_{Ω} 1 / 2 | \nabla x (y) | ² - G (y, x (y)) d y$ . We develop a duality theory and formulate the variational principle for this problem. As a consequence of duality, we derive the variational principle for minimizing sequences of J. We consider the case when G is subquadratic at infinity.

Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita, Takashi Suzuki (2004)

Banach Center Publications

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The non-local Gel’fand problem, $Δ v + λ e^{v} / \int_{Ω} e^{v} d x = 0$ with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

Displaying similar documents to “Erratum for “Generalized dirichlet series and B -functions””

Displaying similar documents to “Erratum for “Generalized dirichlet series and $B$ -functions””