Journal of Operator Theory

Volume 67, Issue 1, Winter 2012 pp. 33-72.

Sectorial forms and degenerate differential operators

Authors: W. Arendt (1) and A.F.M. ter Elst (2)
Author institution: (1) Institute of Applied Analysis, University of Ulm, 89081 Ulm, Germany
(2) Department of Mathematics, University of Auckland, Auckland, 1142, New Zealand

Summary: If $a$ is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with~$a$. This allows us to remove in several theorems of semigroup theory the assumption that the form is closed or symmetric. Many examples are provided, ranging from complex sectorial differential operators, to Dirichlet-to-Neumann operators and operators with Robin or Wentzell boundary conditions.

Keywords: Sectorial forms, semigroups, Dirichlet-to-Neumann operator, degenerate operators, $m$-sectorial operators, boundary conditions

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