✦ LIBER ✦

On the Hadamard products of schlicht functions

✍ Scribed by Q. I. Rahman; J. Stankiewicz

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 344 KB
Volume: 106
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19821060102

No coin nor oath required. For personal study only.

✦ Synopsis

A function q ( z ) is said to be convex if it is a univalent conformal mapping of the unit disk 1x1 -= 1, hereafter called U , onto a convex domain. The HADAMARD product or convolution of two power series f ( 2 ) : = anzn and g(x) : = b,znis defined as the power series (f*g) ( x ) : = anb,xn. The following result was conjectured by

P ~L Y A

and SCHOENBERG [3] and proved by RUSCHEWEYH and SHELL-SMIALL [ 5 ] .

📜 SIMILAR VOLUMES

Generalizations of Hadamard Products of

Generalizations of Hadamard Products of Functions with Negative Coefficients

✍ Jae Ho Choi; Yong Chan Kim; Shigeyoshi Owa 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 113 KB

Let T T n be the class of functions with negative coefficients which are analytic Ž . Ž . Ž . in the unit disk U U. For functions f z and f z belonging to T T n , generaliza-1 2 Ž . Ž . Ž .Ž . tions of the Hadamard product of f z and f z represented by f ^f p,q; z 1 2 1 2 are introduced. In the pres

On the Asymptotic Expansion of Hadamard

On the Asymptotic Expansion of Hadamard Products

✍ Andreas Sauer 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 304 KB

We consider functions f and g which are holomoxphic on closed sectors in 4: where they admit an asymptotic representation at 00 in the form of power series in z-' . We give a simple geometrical condition under which the Hadamard product f \* g of f and g porsemes again an ~y m p totic expansion at 0

Local Schlichtness of a Function Meromor

Local Schlichtness of a Function Meromorphic in the Disk

✍ Shinji Yamashita 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB

On the asymptotic existence of complex H

On the asymptotic existence of complex Hadamard matrices

✍ R. Craigen; W. H. Holzmann; H. Kharaghani 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB 👁 2 views

Let N = N (q) be the number of nonzero digits in the binary expansion of the odd integer q. A construction method is presented which produces, among other results, a block circulant complex Hadamard matrix of order 2 α q, where α ≥ 2N -1. This improves a recent result of Craigen regarding the asympt

On the classification of Hadamard matric

On the classification of Hadamard matrices of order 32

✍ H. Kharaghani; B. Tayfeh-Rezaie 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 100 KB 👁 1 views

## Abstract All equivalence classes of Hadamard matrices of order at most 28 have been found by 1994. Order 32 is where a combinatorial explosion occurs on the number of Hadamard matrices. We find all equivalence classes of Hadamard matrices of order 32 which are of certain types. It turns out that

Bounds on the number of Hadamard designs

Bounds on the number of Hadamard designs of even order

✍ Clement Lam; Sigmund Lam; Vladimir D. Tonchev 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB

## Abstract A new lower bound on the number of non‐isomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2__n__ given in [12] by a factor of 8__n__ − 1 for every odd __n__ > 1, and for every even __n__ such that 4_