We obtain several interesting subordination results for a class of analytic functions defined by using a generalized integral operator. Keywords—Analytic functions, Hadamard product, Subordinating factor sequence

Let C be an arithmetic circuit of size s, given as input that computes a polynomial \(f\in {\mathbb {F}}[x_1,x_2,\ldots ,x_n]\), where \({\mathbb {F}}\) is finite field or the rationals. Using Hadamard product polynomials, we obtain new algorithms for following two problems first studied by Koutis and Williams (Faster algebraic path packing problems, 2008, https://doi.org/10.1007/978-3-540-7057...

Some bounds for the spectral radius of the Hadamard product of two nonnegative matrices are given. Some results involve M -matrices.

Direct arguments are presented showing that for rational series in several com muting variables the rational series problem is non computable and closure under Hadamard product fails

Say that A is a Hadamard factorization of the identity In of size n if A ◦AT = In, where ◦ denotes the Hadamard or entrywise product, and AT denotes the transpose of A. As n = rk(In) = rk(A ◦ AT ) ≤ rk(A)2, it is clear that the rank of any Hadamard factorization of the identity must be at least √ n. Dietzfelbinger et al. [DHS96] raised the question if this bound can be achieved, and showed a bo...