This chapter discusses the elementary properties of functions of several complex variables. It defines analytic functions as the solutions of the Cauchy-Riemann equationsu = 0. After decomposing differential fo
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. ...
Functions of complex variablesOLD AND YOUNG SS PRESSED A RIGHT- OR LEFT-HANDED KEY IN RESPONSE TO THE ONSET OF 1 OF A PAIR OF LIGHTS. IN EXP. I, A WARNING LIGHT INDICATED THE APPROACHING ONSET OF THE STIMULUS LIGHT BUT ALSO COMMUNICATED THE RULE GOVERNING THE ENSUING RESPONSE; I.E., ...
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....
V.AnalyticFunctionsofSeveralComplexVariables TheJacobiinversiontheoremleadstofunctionsofseveralvariableswithmanyperi- ods.So,weareledtotheproblemofdevelopingatheoryofthemwhichisanalogous tothetheoryofellipticfunctions.Firstofall,weneedtogiveanintroductiontothe theoryoffunctionsofseveralcomplexvariables.Inthischapter,...
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; ...
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FunctionsofSeveralVariables FunctionofTwoVariables:15.1p841LetDbeasetof orderedpairsofrealnumbers.Iftoeachorderedpair (x,y)inDtherecorrespondsarealnumberf(x,y), thenfiscalledafunctionofxandy.ThesetDis thedomainoff,andthecorrespondingsetofvalues forf(x,y)istherangeoff. FunctionofThreeVariables:15.1p841For...