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Fully starlike and fully convex harmonic mappings of order α

Sumit Nagpal, V. Ravichandran (2013)

Annales Polonici Mathematici

The hereditary properties of convexity and starlikeness for conformal mappings do not generalize to univalent harmonic mappings. This failure leads to the notions of fully starlike and fully convex mappings. In this paper, properties of fully starlike mappings of order α and fully convex mappings of order α (0 ≤ α < 1) are studied; in particular, the bounds for the radius of full starlikeness of order α as well as the radius of full convexity of order α are determined for certain families of...

Funciones unimodulares y acotación uniforme.

J. Fernández, S. Hui, Harold S. Shapiro (1989)

Publicacions Matemàtiques

In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.

Function theory in sectors

Brian Jefferies (2004)

Studia Mathematica

It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of n + 1 that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in n + 1 .

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