Linear Operators: Spectral theory |
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Page 1105
... follows immediately from ( a ) . Thus , we have only to prove the trilinear inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof ...
... follows immediately from ( a ) . Thus , we have only to prove the trilinear inequality ( a ) for operators in a d - dimensional Hilbert space . Arguing as in the paragraphs of the proof of Lemma 14 following formula ( 3 ) of that proof ...
Page 1226
... follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed symmetric extension . This fact leads us to make the following ...
... follows immediately from part ( a ) and Lemma 5 ( c ) . Q.E.D. It follows from Lemma 6 ( b ) that any symmetric operator with dense domain has a unique minimal closed symmetric extension . This fact leads us to make the following ...
Page 1469
... follows immediately from Theorems 4.1 , 4.2 , and XII.7.2 that ( Tf , f ) = ( Tef , f ) ≥ ( 20 - ε / 2 ) | f2 for f ... follows immediately from the preceding lemma . To prove statement ( b ) , note that is finite below 2 , but not ...
... follows immediately from Theorems 4.1 , 4.2 , and XII.7.2 that ( Tf , f ) = ( Tef , f ) ≥ ( 20 - ε / 2 ) | f2 for f ... follows immediately from the preceding lemma . To prove statement ( b ) , note that is finite below 2 , but not ...
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