Linear Operators: Spectral theory |
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Page 1270
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
Page 1290
... operator n di i Z ( − 1 ) ( 1 ) Pi ( t ) dt dt Σ i = 0 is formally self adjoint provided only that the coefficients p¿ are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) ...
... operator n di i Z ( − 1 ) ( 1 ) Pi ( t ) dt dt Σ i = 0 is formally self adjoint provided only that the coefficients p¿ are real . In the same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt ) ...
Page 1548
... adjoint operator in Hilbert space H1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in H = H1 → H2 by setting D ( T ) = D ( T1 ) → D ( T2 ) and Tx - T ( x1 → x2 ) : = Ꭲ " , Ꮎ Ꭲ 2 , 1 x = D ( T ) ...
... adjoint operator in Hilbert space H1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in H = H1 → H2 by setting D ( T ) = D ( T1 ) → D ( T2 ) and Tx - T ( x1 → x2 ) : = Ꭲ " , Ꮎ Ꭲ 2 , 1 x = D ( T ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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