Certain algebras generated by the multidimensonal analogue of the Bitsadze operator (Q1107081)

Let \(S^{n-1}\) denote the sphere in \(R^ n\). Let K be the operator defined on \(L^ 2(S^{n-1})\) by the formula \(K=A'I+A''P_ n+T\), where A is a matrix-function defined on \(C(S^{n-1})\), T is a compact operator and \(P_ n\) is a multidimensional analogue of the Bitsadze operator. A few theorems which characterize the operator K are given. It is proved, among others that K is Noether operator iff det \(A_ i\neq 0\) \((i=1,2)\), where \(A_ 1=A'+A''\), \(A_ 2=A'-A''\).