Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 66
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 1231
... follows immediately from Definition 14 and Definition 4. Statement ( b ) follows immediately from Definition 14 and Lemma 15. By Lemma 8 ( c ) { x , y } = 0 for x in D ( T * ) and y in D ( T ) . It follows that { x , D ( T ) = 0 if and ...
... follows immediately from Definition 14 and Definition 4. Statement ( b ) follows immediately from Definition 14 and Lemma 15. By Lemma 8 ( c ) { x , y } = 0 for x in D ( T * ) and y in D ( T ) . It follows that { x , D ( T ) = 0 if and ...
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