A UNITARY INVARIANT OF A SEMI-BOUNDED OPERATOR IN RECONSTRUCTION OF MANIFOLDS

作者：Belishev M I^*

来源：Journal of Operator Theory, 2013, 69(2): 299-326.

DOI：10.7900/jot.2010oct22.1925

• Symmetric semi-bounded operator
• lattice with inflation
• evolutionary dynamical system
• wave spectrum
• reconstruction of manifolds

Let L-0 be a densely defined symmetric semi-bounded operator of non-zero defect indexes in a separable Hilbert space H. With L-0 we associate a topological space Omega(L0) (wave spectrum) constructed from the reachable sets of a dynamical system governed by the equation u(tt) (L-0)*u = 0. Wave spectra of unitary equivalent operators are homeomorphic. %26lt;br%26gt;In inverse problems, one needs to recover a Riemannian manifold Omega via dynamical or spectral boundary data. We show that for a generic class of manifolds, Omega is isometric to the wave spectrum Omega(L0) of the minimal Laplacian L-0 = -Delta vertical bar(c0 infinity(Omega\partial derivative Omega)) acting in H = L-2(Omega). In the mean time, L-0 is determined by the inverse data up to unitary equivalence. Hence, the manifold can be. recovered by the scheme %26quot;data double right arrow L-0 double right arrow Omega(L0) (isom)(=) Omega%26quot;.

• 出版日期2013