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Hyperbolically convex functions II

William Ma, David Minda (1999)

Annales Polonici Mathematici

Unlike those for euclidean convex functions, the known characterizations for hyperbolically convex functions usually contain terms that are not holomorphic. This makes hyperbolically convex functions much harder to investigate. We give a geometric proof of a two-variable characterization obtained by Mejia and Pommerenke. This characterization involves a function of two variables which is holomorphic in one of the two variables. Various applications of the two-variable characterization result in...

Hyperbolicity of the Complement of Plane Curves.

Hans Grauert, Ulrike Peternell (1985)

Manuscripta mathematica

Hyperbolische Komplexe Räume und die Vermutung von Mordell.

Dieter Riebesehl (1981)

Mathematische Annalen

Hypercomplex algebras, hypercomplex analysis and conformal invariance

John Ryan (1987)

Compositio Mathematica

Hypercyclic and chaotic weighted shifts

K.-G. Grosse-Erdmann (2000)

Studia Mathematica

Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors $(e_{n})$ form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.

Hypercyclicity of special operators on Hilbert function spaces

Bahmann Yousefi, S. Haghkhah (2007)

Czechoslovak Mathematical Journal

In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.

Hyperelliptic action integral

Bernhard Elsner (1999)

Annales de l'institut Fourier

Applying the “exact WKB method” (cf. Delabaere-Dillinger-Pham) to the stationary one-dimensional Schrödinger equation with polynomial potential, one is led to a multivalued complex action-integral function. This function is a (hyper)elliptic integral; the sheet structure of its Riemann surface above the plane of its values has interesting properties: the projection of its branch-points is in general a dense subset of the plane, and there is a group of symmetries acting on the surface. The distribution...

In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.

Hypertranscendency of conjugacies in complex dynamics.

Paul-Georg Becker, Walter Bergweiler (1995)