Support of CR-hyperfunctions
The aim of this paper is to present a possible shape of the support of CR functions on a generic CR submanifold. Let X be an m-dimensional complex manifold and let N be a k-codimensional, generic, CR, and real analytic submanifold (0\(\leq k\leq m)\). The complexification of N is denoted by Y. A hyperfunction h on N is called a CR function if it satisfies the tangential Cauchy-Riemann system \({\bar \partial}_ b\). A real analytic submanifold L of N is said to be totally characteristic if \(\sqrt{- 1}T^*_ LN\subset \sqrt{-1}T^*N\subset SS({\bar \partial}_ b).\) Here SS(\({\bar \partial}_ b)\) means the characteristic variety of \({\bar \partial}_ b\). Then we have the following theorem. Let \(h\) be a non-zero CR hyperfunction on N. If \(L=\sup p(h)\) is a real analytic submanifold of N, then L is totally characteristic.
support of CR functions on a generic CR submanifold
scientific article; zbMATH DE number 4086039