Generalized Schur Functions as Multivalent Functions
نویسندگان
چکیده
The multivalency approach to generalized Nevanlinna functions established in Wietsma (Indag Math 29:997–1008, 2018) is here extended the related class of Schur giving thereby rise new characterizations for this as well a straightforward function-theoretical proof its factorization. In particular, explains how well-known factorizations two mentioned classes differ from each other. Indeed, by factorization obtained which more directly connected functions. These results demonstrate that valuable concept complete understanding
منابع مشابه
Generalized Integral Operator and Multivalent Functions
Let A(p) be the class of functions f : f(z) = z + ∑∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1(z) = z p (1−z)n+p . We define f (−1) n+p−1(z) by using convolution ? as fn+p−1(z) ? f (−1) n+p−1(z) = z (1−z)n+p . A function p, analytic in E with p(0) = 1, is in the class Pk(ρ) if ∫ 2π 0 ∣∣∣Rep(z)−ρ p−ρ ∣∣∣ dθ ≤ kπ, where z = re, k ≥ 2 and 0 ≤ ρ < p. We use t...
متن کاملBoundary Angular Derivatives of Generalized Schur Functions
Characterization of generalized Schur functions in terms of their Taylor coefficients was established by M. G. Krein and H. Langer in [14]. We establich a boundary analog of this characterization.
متن کاملGeneralized Schur-concave functions and Eaton triples
Motivated by Schur-concavity, we introduce the notion of G-concavity where G is a closed subgroup of the orthogonal group O(V ) on a finite dimensional real inner product space V . The triple (V,G, F ) is an Eaton triple if F ⊂ V is a nonempty closed convex cone such that (A1) Gx ∩ F is nonempty for each x ∈ V . (A2) maxg∈G(x, gy) = (x, gy) for all x, y ∈ F . If W := spanF and H := {g|W : g ∈ G...
متن کاملSchur Functions
Editorial comments. The Schur functions sλ are a special basis for the algebra of symmetric functions Λ. They are also intimately connected with representations of the symmetric and general linear groups. In what follows we will give two alternative definitions of these functions, show how they are related to other symmetric function bases, explicitly describe their connection with representati...
متن کاملSkew Quasisymmetric Schur Functions and Noncommutative Schur Functions
Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2021
ISSN: ['1661-8254', '1661-8262']
DOI: https://doi.org/10.1007/s11785-020-01071-6