Displaying similar documents to “The Schwarz-Pick theorem and its applications”

The Schwarz-Pick theorem and its applications

M. A. Qazi, Q. I. Rahman (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmen-Lindelof principle, which is of course standard in such situations.

Equivalence of analytic and rational functions

J. Bochnak, M. Buchner, W. Kucharz (1997)

Annales Polonici Mathematici

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We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

Failure of analytic hypoellipticity in a class of differential operators

Ovidiu Costin, Rodica D. Costin (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For the hypoelliptic differential operators P = ∂ x 2 + x k ∂ y - x l ∂ t 2 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of k and l left open in the analysis, the operators P also fail to be analytic hypoelliptic (except for ( k , l ) = ( 0 , 1 ) ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.

Intersection theory and separation exponent in complex analytic geometry

Ewa Cygan (1998)

Annales Polonici Mathematici

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We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.

Analytic functions in the unit disc sharing values in a sector

Hong-Yan Xu, Ting-Bin Cao (2012)

Annales Polonici Mathematici

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We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).