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The Cauchy kernel for cones

Sławomir Michalik (2004)

Studia Mathematica

A new representation of the Cauchy kernel Γ for an arbitrary acute convex cone Γ in ℝⁿ is found. The domain of holomorphy of Γ is described. An estimation of the growth of Γ near the singularities is given.

The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space H p , q , α ( U ⁿ ) of the polydisc onto the mixed norm space H p , q , | α | + ( p / q + 1 ) ( n - 1 ) ( U ) of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

The distribution of extremal points for Kergin interpolations : real case

Thomas Bloom, Jean-Paul Calvi (1998)

Annales de l'institut Fourier

We show that a convex totally real compact set in ℂ n admits an extremal array for Kergin interpolation if and only if it is a totally real ellipse. (An array is said to be extremal for K when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on K ) to the interpolated function as soon as it is holomorphic on a neighborhood of K .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence is investigated....

The effect of rational maps on polynomial maps

Pierrette Cassou-Noguès (2001)

Annales Polonici Mathematici

We describe the polynomials P ∈ ℂ[x,y] such that P ( 1 / v ⁿ , A ₁ v ⁿ + A ₂ v 2 n + . . . + A m - 1 v n ( m - 1 ) + v n m - k w ) ∈ ℂ [ v , w ] . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.

The extended future tube conjecture for SO(1, 𝑛 )

Peter Heinzner, Patrick Schützdeller (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let C be the open upper light cone in ℝ 1 + n with respect to the Lorentz product. The connected linear Lorentz group SO ℝ ( 1 , n ) 0 acts on C and therefore diagonally on the N -fold product T N where T = ℝ 1 + n + i C ⊂ ℂ 1 + n . We prove that the extended future tube SO ℂ ( 1 , n ) · T N is a domain of holomorphy.

The field of Nash functions and factorization of polynomials

Stanisław Spodzieja (1996)

Annales Polonici Mathematici

The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.

Currently displaying 21 – 40 of 107