1. See also Extensions of symmetric operators and unbounded operator. 2. This form also makes visible that the skew symmetric operator introduces error when the velocity field diverges. 3. Symmetric operators which are not essentially self-adjoint may still have a canonical self-adjoint extension.4. Therefore finding self-adjoint extension for a positive symmetric operator becomes a " matrix completion problem ". 5. He contributed also to the classical eigenvalue problem for symmetric operators , introducing the method of orthogonal invariants. 6. The compact symmetric operator " G " then has a countable family of eigenvectors which are complete in. 7. A symmetric operator has a unique self-adjoint extension if and only if both its deficiency indices are zero. 8. He established the spectral theory for bounded symmetric operators in a form very much like that now regarded as standard. 9. In the symmetric case, the closedness requirement poses no obstacles, since it is known that all symmetric operators are closable .) 10. Such is the case for " non-negative " symmetric operators ( or more generally, operators which are bounded below ).
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