In this chapter, we shall define holomorphic functions of several complex variables. The essentially local theory given in Chapter 1, §§3, 4 extends to these functions with little effort. We shall then prove two theorems which show that the behavior of functions of n complex variables, with...
In Section 1.1 we define holomorphic functions of several complex variables and prove simple properties of these functions. In Section 1.2, by means of a simple extension of the Cauchy-Green formula to several variables, we solve the inhomogeneous Cauchy-Riemann equations for some special cases. ...
Mathematics - Complex VariablesWe define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then characterize meromorphic functions ...
Wiman-Valiron theory for entire functions of several complex variables. Ph.D. Dissertation. Cornell Univ., Ithaca (1965).A. Schumitzky, A probabilistic approach to the Wiman-Valiron theory for entire functions of several complex variables, Complex Variables, 13 (1989), 85-98....
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Syllabus ofMathematics and Applied Mathematicsat Haide College Functions of Complex Variables Description The theory of functions of a complex variable is a basic branch of mathematics.Itsstudiedobject is the functionsofacomplex variable.The theory of functions of a complex variable has a long history,...
FunctionsofSeveralVariables FunctionofTwoVariables:15.1p841LetDbeasetof orderedpairsofrealnumbers.Iftoeachorderedpair (x,y)inDtherecorrespondsarealnumberf(x,y), thenfiscalledafunctionofxandy.ThesetDis thedomainoff,andthecorrespondingsetofvalues forf(x,y)istherangeoff. FunctionofThreeVariables:15.1p841For...
A.R. Mirotin, Properties of Bernstein functions of several complex variables, Mat. Zametki, 93, 2 (2013), 257 265; English transl.: Math. Notes, 93, 2 (2013).A. R. MIROTIN, Properties of Bernstein functions of several complex variables, Mat. Zametki, 93, 2 (2013), 257-265; ...