A Symmetric Functional Calculus for Systems of Operators of Type ω
نویسنده
چکیده
For a system A = (A1, . . . , An) of linear operators whose real linear combinations have spectra contained in a fixed sector in C and satisfy resolvent bounds there, functions f(A) of the system A of operators can be formed for monogenic functions f having decay at zero and infinity in a corresponding sector in R. In the case that the operators A1, . . . , An commute with each other and satisfy square function estimates in Hilbert space, the correspondence between bounded monogenic functions defined in a sector in R and bounded holomorphic functions defined in a sector in C is used to define the functional calculus f → f(A) for bounded holomorphic functions f in a sector of C. The treatment includes the Dirac operator on a Lipschitz surface in R.
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