Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 85
Page 898
... Corollary 4 follows immediately from Theorem 1 and Corollary IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associat- ed , in Corollary 4 , with the normal operator T is called the resolution of the identity for T ...
... Corollary 4 follows immediately from Theorem 1 and Corollary IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associat- ed , in Corollary 4 , with the normal operator T is called the resolution of the identity for T ...
Page 1301
... corollary were false , it would follow that τ has a boundary value at a which is independent of the set Ao , ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. T ...
... corollary were false , it would follow that τ has a boundary value at a which is independent of the set Ao , ... , An - 1 and hence has at least n + 1 independent boundary values at a . But this is impossible by Corollary 22. Q.E.D. T ...
Page 1459
... COROLLARY . A formally positive formally symmetric formal differential operator τ is finite below zero . PROOF . It is obvious from Definition 20 that 7 is bounded below . Thus the present corollary follows from Corollary 7 and ...
... COROLLARY . A formally positive formally symmetric formal differential operator τ is finite below zero . PROOF . It is obvious from Definition 20 that 7 is bounded below . Thus the present corollary follows from Corollary 7 and ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero