Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 79
Page 955
... linear functional h , and since , by IX.2.3 , every such function is continuous , it follows that a multiplicative linear functional on A is entirely determined by its restriction to A 。. Thus , there is a unique point P. in M such ...
... linear functional h , and since , by IX.2.3 , every such function is continuous , it follows that a multiplicative linear functional on A is entirely determined by its restriction to A 。. Thus , there is a unique point P. in M such ...
Page 1293
... function g in H ( I ) such that r * g = w , and the assertion reduces to So f ( t ) x * g ( t ) dt = 0 which is the hypothesis of the theorem . ( E ) Suppose now that some linear functional on L2 ( I ) , represented by a function h ...
... function g in H ( I ) such that r * g = w , and the assertion reduces to So f ( t ) x * g ( t ) dt = 0 which is the hypothesis of the theorem . ( E ) Suppose now that some linear functional on L2 ( I ) , represented by a function h ...
Page 1303
... linear functional on the Hilbert space D ( T1 ( 7 ) ) . If lim , → B¿ ( ƒ ) B ( f ) exists for each fin D ( T , ( T ) ) , then , by Theorem II.1.17 , B is a continuous linear func- tional on D ( T , ( t ) ) . Clearly B ( f ) = 0 for ...
... linear functional on the Hilbert space D ( T1 ( 7 ) ) . If lim , → B¿ ( ƒ ) B ( f ) exists for each fin D ( T , ( T ) ) , then , by Theorem II.1.17 , B is a continuous linear func- tional on D ( T , ( t ) ) . Clearly B ( f ) = 0 for ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero