Homogeneous extremal function for a ball in ℝ²

Mirosław Baran

Displaying similar documents to “Homogeneous extremal function for a ball in ℝ²”

Alexander’s projective capacity for polydisks and ellipsoids in $ℂ^{N}$

Mieczysław Jędrzejowski (1995)

Annales Polonici Mathematici

Similarity:

Alexander’s projective capacity for the polydisk and the ellipsoid in $ℂ^{N}$ is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in $ℂ^{N}$ are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in $ℂ^{N}$ is proved to have an asymptotic behaviour in $ℂ^{N}$ similar to that of the Siciak homogeneous extremal function associated with K.

Hamilton sequences and extremality for certain Teichmüller mappings.

Yao, Guowu (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

The homogeneous transfinite diameter of a compact subset of $ℂ^{N}$

Mieczysław Jędrzejowski (1991)

Annales Polonici Mathematici

Similarity:

Let K be a compact subset of $ℂ^{N}$ . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of $ℂ^{N}$ is computed.

Some subclasses of close-to-convex functions

Adam Lecko (1993)

Annales Polonici Mathematici

Similarity:

For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes $C_{β} (α)$ defined as follows: a function f regular in U = z: |z| < 1 of the form $f (z) = z + \sum_{n = 1}^{\infty} a_{n} z^{n}$ , z ∈ U, belongs to the class $C_{β} (α)$ if $R e e^{i β} (1 - α ² z ²) f^{'} (z) < 0$ for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in $C_{β} (α)$ are examined.

Counting irreducible polynomials over finite fields

Qichun Wang, Haibin Kan (2010)

Czechoslovak Mathematical Journal

Similarity:

In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following theorem: $π (x) = \frac{q}{q - 1} \frac{x}{{log}_{q} x} + \frac{q}{{(q - 1)}^{2}} \frac{x}{{log}_{q}^{2} x} + O (\frac{x}{{log}_{q}^{3} x}), x = q^{n} \to \infty$ where $π (x)$ denotes the number of monic irreducible polynomials in $F_{q} [t]$ with norm $\leq x$ .

On the growth of entire functions with zero sets having infinite exponent of convergence.

Miles, Joseph (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

Similarity:

On the mean value of the generalized Dirichlet $L$ -functions

Rong Ma, Yuan Yi, Yulong Zhang (2010)

Czechoslovak Mathematical Journal

Similarity:

Let $q \geq 3$ be an integer, let $χ$ denote a Dirichlet character modulo $q .$ For any real number $a \geq 0$ we define the generalized Dirichlet $L$ -functions $L (s, χ, a) = \sum_{n = 1}^{\infty} \frac{χ (n)}{{(n + a)}^{s}},$ where $s = σ + i t$ with $σ > 1$ and $t$ both real. They can be extended to all $s$ by analytic continuation. In this paper we study the mean value properties of the generalized Dirichlet $L$ -functions especially for $s = 1$ and $s = \frac{1}{2} + i t$ , and obtain two sharp asymptotic formulas by using the analytic method and the theory of van der Corput.

Estimates in the Hardy-Sobolev space of the annulus and stability result

Imed Feki (2013)

Czechoslovak Mathematical Journal

Similarity:

The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space $H^{k, \infty}$ ; $k \in ℕ^{*}$ of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L. Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S. Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev...