Displaying similar documents to “A study of various results for a class of entire Dirichlet series with complex frequencies”

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 ) = n = 1 a n - s with | | f | | : = s u p s > 0 | f ( s ) | < , then n = 1 | a | n - 2 | | f | | and even slightly better, and n = 1 | a | n - 1 / 2 C | | f | | , C being an absolute constant.

On discrete mean values of Dirichlet L -functions

Ertan Elma (2021)

Czechoslovak Mathematical Journal

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Let χ be a nonprincipal Dirichlet character modulo a prime number p 3 and let 𝔞 χ : = 1 2 ( 1 - χ ( - 1 ) ) . Define the mean value p ( - s , χ ) : = 2 p - 1 ψ ( mod p ) ψ ( - 1 ) = - 1 L ( 1 , ψ ) L ( - s , χ ψ ¯ ) ( σ : = s > 0 ) . We give an identity for p ( - s , χ ) which, in particular, shows that p ( - s , χ ) = L ( 1 - s , χ ) + 𝔞 χ 2 p s L ( 1 , χ ) ζ ( - s ) + o ( 1 ) ( p ) for fixed 0 < σ < 1 2 and | t : = s | = o ( p ( 1 - 2 σ ) / ( 3 + 2 σ ) ) .

Stević-Sharma type operators on Fock spaces in several variables

Lijun Ma, Zicong Yang (2024)

Czechoslovak Mathematical Journal

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Let ϕ be an entire self-map of N , u 0 be an entire function on N and 𝐮 = ( u 1 , , u N ) be a vector-valued entire function on N . We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator T u 0 , 𝐮 , ϕ as follows: - . 4 p t T u 0 , 𝐮 , ϕ f = u 0 · f ϕ + i = 1 N u i · f z i ϕ . We investigate the boundedness and compactness of T u 0 , 𝐮 , ϕ on Fock spaces. The complex symmetry and self-adjointness of T u 0 , 𝐮 , ϕ are also characterized.

The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu (2017)

Commentationes Mathematicae Universitatis Carolinae

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ϵ Y have the w G P property, when X and Y have the w G P property.

Nonvanishing of a certain Bernoulli number and a related topic

Humio Ichimura (2013)

Acta Arithmetica

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Let p = 1 + 2 e + 1 q be an odd prime number with q an odd integer. Let δ (resp. φ) be an odd (resp. even) Dirichlet character of conductor p and order 2 e + 1 (resp. order d φ dividing q), and let ψₙ be an even character of conductor p n + 1 and order pⁿ. We put χ = δφψₙ, whose value is contained in K = ( ζ ( p - 1 ) p ) . It is well known that the Bernoulli number B 1 , χ is not zero, which is shown in an analytic way. In the extreme cases d φ = 1 and q, we show, in an algebraic and elementary manner, a stronger nonvanishing result: T r n / 1 ( ξ B 1 , χ ) 0 for any...

On the characterization of harmonic functions with initial data in Morrey space

Bo Li, Jinxia Li, Bolin Ma, Tianjun Shen (2024)

Czechoslovak Mathematical Journal

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Let ( X , d , μ ) be a metric measure space satisfying the doubling condition and an L 2 -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on X . We will show that a solution u to ( - t 2 + ) u = 0 on X × + satisfies an α -Carleson condition if and only if u can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space L 2 , α ( X ) , where α is a nonnegative function defined on a class of balls in X . This result extends the analogous characterization...

Variations on a question concerning the degrees of divisors of x n - 1

Lola Thompson (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we examine a natural question concerning the divisors of the polynomial x n - 1 : “How often does x n - 1 have a divisor of every degree between 1 and n ?” In a previous paper, we considered the situation when x n - 1 is factored in [ x ] . In this paper, we replace [ x ] with 𝔽 p [ x ] , where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p .

-sums and the Banach space / c

Christina Brech, Piotr Koszmider (2014)

Fundamenta Mathematicae

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This paper is concerned with the isomorphic structure of the Banach space / c and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that / c does not have an orthogonal -decomposition, that is, it is not of the form ( X ) for any Banach space X. The main local result is that it is consistent that ( c ( ) ) does not embed isomorphically into / c , where is the cardinality of the continuum,...

Estimates near the boundary for second order derivatives of solutions of the Dirichlet problem for the biharmonic equation

Vladimir A. Kondratiev, Olga A. Oleinik (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Per ogni soluzione della (1) nel dominio limitato Ω ,, appartenente a H 0 2 ( Ω ) e soddisfacente le condizioni (2), si dimostra la maggiorazione (5), valida nell'intorno di ogni punto x 0 del contorno; si consente a Ω di essere singolare in x 0 .

Generalized versions of Ilmanen lemma: Insertion of C 1 , ω or C loc 1 , ω functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space X , if f 1 : X is continuous and semiconvex with modulus ω , f 2 : X is continuous and semiconcave with modulus ω and f 1 f 2 , then there exists f C 1 , ω ( X ) such that f 1 f f 2 . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ω ( t ) = t ) to the case of an arbitrary nontrivial modulus ω . This generalization (where a C l o c 1 , ω function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

Spectral condition, hitting times and Nash inequality

Eva Löcherbach, Oleg Loukianov, Dasha Loukianova (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Let X be a μ -symmetric Hunt process on a LCCB space 𝙴 . For an open set 𝙶 𝙴 , let τ 𝙶 be the exit time of X from 𝙶 and A 𝙶 be the generator of the process killed when it leaves 𝙶 . Let r : [ 0 , [ [ 0 , [ and R ( t ) = 0 t r ( s ) d s . We give necessary and sufficient conditions for 𝔼 μ R ( τ 𝙶 ) l t ; in terms of the behavior near the origin of the spectral measure of - A 𝙶 . When r ( t ) = t l , l 0 , by means of this condition we derive the Nash inequality for the killed process. In the diffusion case this permits to show that the existence of moments of order l + 1 for τ 𝙶 ...