Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 69
Page 898
... resolution of the identity for T. In order to relate this notion of the resolution of the identity with that given in Section 1 we state the following corollary . 6 COROLLARY . If E is the resolution of the identity for the normal ...
... resolution of the identity for T. In order to relate this notion of the resolution of the identity with that given in Section 1 we state the following corollary . 6 COROLLARY . If E is the resolution of the identity for the normal ...
Page 920
... resolution of the identity . The following theorem gives a method for calculating the resolution of the identity for a self adjoint operator T in terms of its resolvent R ( x ; T ) = ( aI - T ) -1 . It should be recalled ( Theorem 4.2 ) ...
... resolution of the identity . The following theorem gives a method for calculating the resolution of the identity for a self adjoint operator T in terms of its resolvent R ( x ; T ) = ( aI - T ) -1 . It should be recalled ( Theorem 4.2 ) ...
Page 1128
... resolution of T is the strong limit of linear combinations of the projections E. This we do as follows . Let A be the commutative B * -algebra of operators generated by the projections E , and let Д be its spectrum . If is any element ...
... resolution of T is the strong limit of linear combinations of the projections E. This we do as follows . Let A be the commutative B * -algebra of operators generated by the projections E , and let Д be its spectrum . If is any element ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero