Theory of Linear Operators in Hilbert SpaceThis classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition. |
Contents
HILBERT SPACE 1 Linear Spaces | 1 |
The Scalar Product | 2 |
Some Topological Concepts | 4 |
Copyright | |
78 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator arbitrary assume bounded linear operator bounded operator Cayley transform characteristic function closure completely continuous operator converges corresponding D₁ deficiency indices defined everywhere definition denote dense in H differential operator domain e₁ eigenvalue eigenvector element f equation everywhere in H exists f₁ fe H finite interval follows function F G₁ H₁ H₂ Hence Hilbert space identity implies inequality inversion formulas isometric operator Lē(a lemma linear envelope linear functional linear manifold linear operator linearly independent Math matrix multiplicity nonzero norm obtain operator defined orthogonal orthonormal system present section projection operator Proof R₁ regular point relation resolvent scalar product self-adjoint extension self-adjoint operator solution space H spectral function spectrum subspace G symmetric operator theorem is proved theory unique unitary operator vector f zero λο Φ λ