On branches at infinity of a pencil of polynomials in two complex variables
Let F ∈ ℂ[x,y]. Some theorems on the dependence of branches at infinity of the pencil of polynomials f(x,y) - λ, λ ∈ ℂ, on the parameter λ are given.
On -symmetrical functions
n the present paper the authors study some families of functions from a complex linear space into a complex linear space . They introduce the notion of -symmetrical function (; ) which is a generalization of the notions of even, odd and -symmetrical functions. They generalize the well know result that each function defined on a symmetrical subset of can be uniquely represented as the sum of an even function and an odd function.
On matrix Reinhardt domains.
On the Forelli-Rudin construction and weighted Bergman projections
On the Mahler measure of polynomials in many variables
On the maximum modulus theorem for nonanalytic functions in several complex variables.
Let w = f(z1, ..., zn) = u(x1, ..., yn) + iv(x1, ..., yn) be a complex function of the n complex variables z1, ..., zn, defined in some open set A ⊂ Cn. The purpose of this note is to prove a maximum modulus theorem for a class of these functions, assuming neither the continuity of the first partial derivatives of u and v with respect to xk and yk, nor the conditions fzk = 0 in A for k = 1, 2, ..., n (the Cauchy-Riemann equations in complex form).
On the theorems of Hartogs and Bishop