Probabilistic Techniques Leading to a Valiron-type Theorem in Several Complex Variables
نویسندگان
چکیده
منابع مشابه
A short introduction to several complex variables
This text is a short two hour introduction into the theory of several complex variables. These lectures were given in May 1996 at Caltech to the class Ma 108 substituting for someone else. As prerequisite, the topic requires some familiarity with complex analysis in one dimension. The higher dimensional generalization of complex analysis in one variables is an important part of mathematics. Our...
متن کاملSome inequalities in connection to relative orders of entire functions of several complex variables
Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.
متن کاملBoundary Problems Leading to Orthogonal Polynomials in Several Variables
where we take formally £_i(x)=0, po(x) — l, and have incorporated suitable constant factors in the pn{x). Conversely [2] we may pass from (1.2) to the existence of at least one spectral function \[/(x) with respect to which (1.1) holds. The position is much less clear in respect to orthogonal polynomials in several variables, for which work has been devoted mainly to the approach which starts w...
متن کاملComplex Dynamics in Several Variables
1. Motivation 117 2. Iteration of Maps 118 3. Regular Versus Chaotic Behavior 119 4. The Horseshoe Map and Symbolic Dynamics 120 5. Hénon Maps 123 6. Properties of Horseshoe and Hénon Maps 126 7. Dynamically Defined Measures 127 8. Potential Theory 129 9. Potential Theory in One-Variable Dynamics 131 10. Potential Theory and Dynamics in Two Variables 133 11. Currents and Applications to Dynamic...
متن کاملBohr’s Power Series Theorem in Several Variables
Generalizing a classical one-variable theorem of Bohr, we show that if an n-variable power series has modulus less than 1 in the unit polydisc, then the sum of the moduli of the terms is less than 1 in the polydisc of radius 1/(3 √ n ). How large can the sum of the moduli of the terms of a convergent power series be? Harald Bohr addressed this question in 1914 with the following remarkable resu...
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: The Annals of Mathematical Statistics
سال: 1970
ISSN: 0003-4851
DOI: 10.1214/aoms/1177696711