On the Fourier-Laplace representation of analytic functions in tube domains.
Sia un endomorfismo olomorfo della palla unitaria aperta di . In questa nota proviamo che certe ipotesi minimali, relative al comportamento di su un orociclo e vicino ad un punto del bordo, assicurano che è un automorfismo olomorfo di .
We give the formula expressing the Łojasiewicz exponent near the fibre of polynomial mappings in two variables in terms of the Puiseux expansions at infinity of the fibre.
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).