Vol. 51, No. 2, 1974

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Laplace transform methods in multivariate spectral theory

Robert F. V. Anderson

Vol. 51 (1974), No. 2, 339–348

The Laplace transform of the semigroup exp(tA) generated by an operator A gives the resolvent of A. An integral formula is obtained for the Laplace transform of exp(tA + B), where B is another operator which does not commute with A. The new transform has analytic continuation to the same domain as the resolvent, but the analytic continuation is not single-valued. The integral formula is then applied to the joint spectral theory of noncommutative operators. Explicit compulations with matrices of degree two illustrate the results.

Mathematical Subject Classification 2000
Primary: 47D05
Secondary: 47A60
Received: 19 November 1971
Published: 1 April 1974
Robert F. V. Anderson