On the capacity of a plane condenser and conformal mapping.
On the characteristic properties of certain optimization problems in complex analysis
We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.
On the class of functions defined in a halfplane and starlike with respect to the boundary point
The purpose of this paper is to study the class of univalent analytic functions defined in the right halfplane ℍ and starlike w.r.t. the boundary point at infinity. An analytic characterization of functions in is presented.
On the class of functions strongly starlike of order α with respect to a point
We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).
On the coefficient bodies of meromorphic univalent functions omitting a disc
Let S(b) be the class of bounded normalized univalent functions and Σ(b) the class of normalized univalent meromorphic functions omitting a disc with radius b. The close connection between these classes allows shifting the coefficient body information from the former to the latter. The first non-trivial body can be determined in Σ(b) as well as the next one in the real subclass .
On the coefficient domains of univalent functions.
On the coefficient problem for univalent functions.
On The Coefficient Structure And A Growth Theorem For The Functions f(z) For Which zf'(z) Is Spirallike
On the coefficients of bounded real univalent functions
On the coefficients of some classes of starlike functions
On the coefficients of starlike functions of some classes
On the coefficients problem of the schlicht function
On the complex zeros of some families of orthogonal polynomials.
On the complexification of real-analytic polynomial mappings of ℝ²
We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.
On the conformal gauge of a compact metric space
In this article we study the Ahlfors regular conformal gauge of a compact metric space , and its conformal dimension . Using a sequence of finite coverings of , we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gauge. We show how to compute using the critical exponent associated to the combinatorial modulus.
On the continuation of quasiisometric mappings.
On the continuity of the Faber mapping
On the Convergence and Divergence of Bairstow's Method.
On the convergence of Halley-like method.
On the convergence of Laplace-Beltrami operators associated to quasiregular mappings