The theory of functions of several complex variables is the branch of mathematics dealing with complex valued functions on the space c n of n tuples of complex numbers as in complex analysis which is the case n 1 but of a distinct character these are not just any functions they are supposed to be holomorphic or complex analytic so that locally speaking they are power series in . This volume is an introductory text in several complex variables using methods of integral representations and hilbert space theory it investigates mainly the studies of the estimate of solutions of the cauchy riemann equations in pseudoconvex domains and the extension of holomorphic functions in . Get this from a library several complex variables and integral formulas kenzo adachi this volume is an introductory text in several complex variables using methods of integral representations and hilbert space theory it investigates mainly the studies of the estimate of solutions . Cauchy integral formula cont inhomogeneous cr equation riemann equation in one variable functions of several complex variables 3 the inhomogeneous cauchy riemann equation in several variables hartogs theorem 4 applying hartogs theorem the dolbeault complex exactness of the dolbeault complex on polydisks 5. 4 complex integration cauchy integral theorem and cauchy integral formulas definite integral of a complex valued function of a real variable consider a complex valued function ft of a real variable t ft ut ivt which is assumed to be a piecewise continuous function defined in the closed interval a t b
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