WHAT is the theory of functions about? This question may be heard now and again from a mathematical student; and if, by way of a pattial reply, it be said that the elements of the theory of functions forms the basis on which the whole of that part of pure mathematics which deals with continuously varying quantity rests, the answer would not be too wide nor would it always imply too much. Theory of Functions of a Complex Variable. By Dr. A. R. Forsyth. (Cambridge University Press, 1893.)

Theory of Functions of a Complex Variable

Measure and category

If f : C ! P n is a holomorphic curve of hyper-order less than one for which 2n + 1 hyperplanes in general position have forward invariant preimages with respect to the translation �(z) = z +c, then f is periodic with period c 2 C. This result, which can be described as a difference analogue of M. Green's Picard-type theorem for holomorphic curves, follows from a more general result presented in this paper. The proof relies on a new version of Cartan's second main theorem for the Casorati determinant and an extended version of the difference analogue of the lemma on the logarithmic derivatives, both of which are proved here. Finally, an application to the uniqueness theory of meromorphic functions is given, and the sharpness of the obtained results is demonstrated by examples.

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Holomorphic curves with shift-invariant hyperplane preimages

Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity

We give a method for constructing transcendental entire functions with good control of both the singular values of f and the geometry of f. Among other applications, we construct a function f with bounded singular set, whose Fatou set contains a wandering domain.

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Constructing entire functions by quasiconformal folding

Characteristics of the behavior of a meromorphic function and the first fundamental theorem Meromorphic functions of finite order The second fundamental theorem Deficient values Asymptotic properties of meromorphic functions and deficiencies Value distribution with respect to the arguments Applications of Riemann surfaces to value distribution On the magnitude of an entire function Notes A survey of some results after 1970 Bibliography References added to the English edition Author index Subject index Notation index.

Value Distribution of Meromorphic Functions

http://yoksis.bilkent.edu.tr/doi_getpdf/articles/10.1006-jmaa.1997.5734.pdf

Analytic and Asymptotic Properties of Generalized Linnik Probability Densities

We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an "abstract" version of this inequality. The approach uses "logarithmic determinants" and new estimates of canonical products of genus one.

Variations on the theme of Marcinkiewicz’ inequality

On the completely regular growth of analytic functions having maximum on a ray by A. M. Ulanovskii Value distribution of sequences of rational functions by M. Sodin Inverse problem for the Sturm-Liouville operator with almost-periodic potential having only positive Fourier exponents by M. Simbirskii Subharmonic functions of completely regular growth in a closed cone by L. I. Ronkin Complete description of the pair indicator-lower indicator of an entire function by L. R. Podoshev Solvability conditions for the homogeneous Riemann boundary problem with an infinite index by I. V. Ostrovskii Completeness of a system of functions on sets in the complex plane by Yu. I. Lyubarskii and V. A. Tkachenko Frames in the Bargmann space of entire functions by Yu. I. Lyubarskii Subharmonic functions of finite degree bounded on subsets of the "real hyperplane" by B. Ya. Levin, V. N. Logvinenko, and M. L. Sodin Uniqueness theorems for algebraic functions by A. A. Goldberg and V. A. Pyana Subharmonic functions and $\cos (\pi \lambda)$-theorems for entire functions represented by gap series by A. E. Fryntov Lacunary series and Fourier integrals of functions of several variables by V. N. Logvinenko and S. Yu. Favorov Parametrization of entire functions of sine-type by their critical values by A. E. Eremenko and M. L. Sodin On stability estimates in the Marcinkiewicz theorem and its generalization by L. B. Golinskii and G. P. Chistyakov Limit sets and multiplicators of entire functions by V. S. Azarin and V. B. Giner.

Entire and subharmonic functions

(1998). Anatolii asirovich gol'dberg. Complex Variables, Theory and Application: An International Journal: Vol. 37, No. 1-4, pp. 1-51.

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Iossif Ostrovskii

Papers

Value Distribution of Meromorphic Functions

Analytic and Asymptotic Properties of Generalized Linnik Probability Densities

Variations on the theme of Marcinkiewicz’ inequality

Entire and subharmonic functions

Anatolii asirovich gol'dberg