Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 71
Page 1187
... operator ( 21 - T ) -1 . The spectrum o ( T ) of T is the complement of the resolvent set p ( T ) . The point spectrum o , ( T ) , the continuous spectrum o 。( T ) , and the residual spectrum σ , ( T ) are defined just as they were in ...
... operator ( 21 - T ) -1 . The spectrum o ( T ) of T is the complement of the resolvent set p ( T ) . The point spectrum o , ( T ) , the continuous spectrum o 。( T ) , and the residual spectrum σ , ( T ) are defined just as they were in ...
Page 1540
... operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( t ) + B . All Let be a regular formal differential operator on ...
... operator on an interval I , and let B be a compact operator in L2 ( I ) . Prove that the essential spectrum of 7 coincides with the essential spectrum of the operator T1 ( t ) + B . All Let be a regular formal differential operator on ...
Page 1612
... operators which are nonselfadjoint , and hence operators to which the spectral theorem of Chapters X and XII does not apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will be ...
... operators which are nonselfadjoint , and hence operators to which the spectral theorem of Chapters X and XII does not apply . The more general theory of spectral operators , to be developed in Chapters XV , XVI , XVII and XVIII will be ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
52 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero