Starlikeness and convexity for analytic functions concerned with Jack's Lemma.
Starlikeness and convexity of a class of analytic functions.
Starlikeness associated with parabolic regions.
Starlikeness conditions for an integral operator.
Starlikeness criteria for odd symmetric analytic functions
We investigate some starlikeness conditions for odd symmetric analytic functions defined in the unit disc.
Starlikeness of functions satisfying a differential inequality
In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.
Starlikeness of polynomials and finite Blaschke products
The radius of starlikeness for polynomial mappings and finite Blaschke products with zeroes distributed at equal angles around a circle centered at the origin, as well as with zeroes concentrated at a single point, are considered, and sharp bounds are obtained. Results expressing the radius of starlikeness of an arbitrary polynomial or Blaschke product in terms of the magnitudes of the zeroes are also given. These are also sharp.
Stieltjes moment problem in general Gelfand-Shilov spaces
The Stieltjes moment problem is studied in the framework of general Gelfand-Shilov spaces, subspaces of the space of rapidly decreasing smooth complex functions, which are defined by imposing suitable bounds on their elements in terms of a given sequence M. Necessary and sufficient conditions on M are stated for the problem to have a solution, sometimes coming with linear continuous right inverses of the moment map, sending a function to the sequence of its moments. On the way, some results on the...
Stochastic continuity and approximation
This work is concerned with the study of stochastic processes which are continuous in probability, over various parameter spaces, from the point of view of approximation and extension. A stochastic version of the classical theorem of Mergelyan on polynomial approximation is shown to be valid for subsets of the plane whose boundaries are sets of rational approximation. In a similar vein, one can obtain a version in the context of continuity in probability of the theorem of Arakelyan on the uniform...
Stochastic Holomorphy.
Stone-Weierstrass theorem
It will be shown that the Stone-Weierstrass theorem for Clifford-valued functions is true for the case of even dimension. It remains valid for the odd dimension if we add a stability condition by principal automorphism.
Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...
Strengthening pseudoconvexity of finite-dimensional Teichmüller spaces.
Strict continuous homomorphisms on spaces of bounded holomorphic functions.
Let HE∞ be the space of all bounded holomorphic functions on the unit ball of the Banach space E. In this note we study the algebra homomorphisms on HE∞ which are strict continuous.
Strict positive definiteness on spheres via disk polynomials.
Strict topologies in non-archimedean function spaces.
Strictly analytic functions on p-adic analytic open sets.
Let K be an algebraically closed complete ultrametric field. M. Krasner and P. Robba defined theories of analytic functions in K, but when K is not spherically complete both theories have the disadvantage of containing functions that may not be expanded in Taylor series in some disks. On other hand, affinoid theories are only defined in a small class of sets (union of affinoid sets) [2], [13] and [17]. Here, we suppose the field K topologically separable (example Cp). Then, we give a new definition...
Strictly decreasing solutions of a class of iterative equations on the unit circle.
Strong -weights and scaling invariant Besov capacities.
Strong asymptotics for extremal polynomials off a complex curve.