In this paper we give some convergence properties of Hadamard product set of polynomials defined by several simple monic sets of several complex variables in complete Reinhardt domains and in hyperelliptical regions too.

For every n divisible by 4, we construct a square matrix H of size n, with coeecients 1, such that H H t nI mod 32. This solves the 32-modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16-modular Golay sequences. 0. Introduction Hadamard matrices can be constructed from various binary sequences, either from Golay complementary sequences, or Williamson...

Making use a linear operator, which is defined here by means of the Hadamard product (or convolution) involving the generalized hypergeometric function, we introduce two novel subclasses Qp,q,s(α1;A,B,λ) and Qp,q,s(α1;A,B,λ) of meromorphically multivalent functions of order λ (0 λ < p) in the punctured disc U∗ . In this paper we investigate the various important properties and characteristics o...

In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this paper, we present a proof for the conjecture. The mathematical tools employed are the second-order multiplexing decimation-Hadamard transform, Stickelberger’...

1. Weierstrass products 2. Poisson-Jensen formula 3. Hadamard products Apart from factorization of polynomials, after Euler's sin πz πz = ∞ n=1 1 − z 2 n 2 there is Euler's product for Γ(z), which he used as the definition of the Gamma function: ∞ 0 e −t t z dt t = Γ(z) = 1 z e γz ∞ n=1 1 + z n e −z/n where the Euler-Mascheroni constant γ is essentially defined by this relation. The integral (E...