Holonomic functions in a polycircle with nonnegative imaginary part
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A well-known theorem of Nevanlinna on the representation of nonnegative measure of a function holomorphic in a circle and having nonnegative imaginary part is extended to functions of many complex variables, holomorphic in a polycircle and having there a nonnegative imaginary part.
KeywordsImaginary Part Complex Variable Nonnegative Measure Holonomic Function Nonnegative Imaginary Part
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- 1.R. Nevanlinna, Analytic Functions, Spring-Verlag (1969).Google Scholar
- 2.V. S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables [in Russian], Moscow (1964).Google Scholar
- 3.G. E. Shilov and B. L. Gurevich. Integral, Measure, and Derivative [in Russian], Moscow (1967).Google Scholar
- 4.L. Schwartz, Mathematics for the Physical Sciences, Addison-Wesley (1967).Google Scholar
- 5.V. S. Vladimirov, “Holomorphic functions with nonnegative imaginary part in a tubular domain under a cone,” Matem. Sb.,79, No. 1, 128–152 (1969).Google Scholar
- 6.V. S. Vladimirov, “Holomorphic functions with positive imaginary part in a tube of the future,” Matem. Sb.,93, No. 1, 3–17 (1974).Google Scholar