Search results for "Holomorphic function"
showing 4 items of 94 documents
Analytic structure in fibers of H∞(Bc0)
2020
Abstract Let H ∞ ( B c 0 ) be the algebra of all bounded holomorphic functions on the open unit ball of c 0 and M ( H ∞ ( B c 0 ) ) the spectrum of H ∞ ( B c 0 ) . We prove that for any point z in the closed unit ball of l ∞ there exists an analytic injection of the open ball B l ∞ into the fiber of z in M ( H ∞ ( B c 0 ) ) , which is an isometry from the Gleason metric of B l ∞ to the Gleason metric of M ( H ∞ ( B c 0 ) ) . We also show that, for some Banach spaces X, B l ∞ can be analytically injected into the fiber M z ( H ∞ ( B X ) ) for every point z ∈ B X .
On holomorphic functions attaining their norms
2004
Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that X has the Radon–Nikodym property. We also show that the same result holds for Banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball. We prove that there exists a polynomial such that for any fixed positive integer k , it cannot be approximated by norm attaining polynomials with degree less than k . For X=d ∗ (ω,1) , a predual of a Lorentz sequence space, we prove that the product of two p…
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
THE ARITHMETIC BOHR RADIUS
2007
We study the arithmetic Bohr radius of Reinhardt domains in ℂ n which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.