Linear Operators, Part 2 |
From inside the book
Results 1-3 of 82
Page 1224
... symmetric then every symmetric extension T2 of T1 , and , in particular , every self adjoint extension of T1 , satisfies TCTCTCT * . 1 1 2 = PROOF . If T1C T2 and y = D ( T * ) , then ( x , T * y ) = ( T2x , y ) ( T1x , y ) for any ...
... symmetric then every symmetric extension T2 of T1 , and , in particular , every self adjoint extension of T1 , satisfies TCTCTCT * . 1 1 2 = PROOF . If T1C T2 and y = D ( T * ) , then ( x , T * y ) = ( T2x , y ) ( T1x , y ) for any ...
Page 1236
... symmetric extension of T is the restriction of T * to the subspace of D ( T * ) determined by a symmetric family of boundary conditions , B ( x ) = 0 , i = 1 , . . . , k . Conversely , every such restriction T1 of T * is a closed ...
... symmetric extension of T is the restriction of T * to the subspace of D ( T * ) determined by a symmetric family of boundary conditions , B ( x ) = 0 , i = 1 , . . . , k . Conversely , every such restriction T1 of T * is a closed ...
Page 1238
... symmetric operator with finite deficiency indices whose sum is p . Let A1 , ... , A , be a complete set of boundary values for T , and let Σ , 1 , A ̧Ã , be the bilinear form of Lemma 23 . A set of boundary conditions 1B , A ( x ) = 0 ...
... symmetric operator with finite deficiency indices whose sum is p . Let A1 , ... , A , be a complete set of boundary values for T , and let Σ , 1 , A ̧Ã , be the bilinear form of Lemma 23 . A set of boundary conditions 1B , A ( x ) = 0 ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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(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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero