Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1224
... symmetric then every symmetric extension T2 of T1 . and , in particular , every self adjoint extension of T1 , satisfies T1CT , CT CT * . 1 2 PROOF . If T1C T2 and y = D ( T * ) , then ( x , T ‡ y ) 1 2 = ( T2x , y ) ( T1x , y ) for any ...
... symmetric then every symmetric extension T2 of T1 . and , in particular , every self adjoint extension of T1 , satisfies T1CT , CT CT * . 1 2 PROOF . If T1C T2 and y = D ( T * ) , then ( x , T ‡ y ) 1 2 = ( T2x , y ) ( T1x , y ) for any ...
Page 1236
... 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. PROOF . We shall prove the second statement first . As each B is a continuous ...
... 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. PROOF . We shall prove the second statement first . As each B is a continuous ...
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 Σ3 ̧ ‚ — ‚ ¤‚‚¡à ̧ be the bilinear form of Lemma 23 . A set of boundary conditions 1B , 4 ̧ ( x ) ...
... symmetric operator with finite deficiency indices whose sum is p . Let A1 , ... , A , be a complete set of boundary values for T , and let Σ3 ̧ ‚ — ‚ ¤‚‚¡à ̧ be the bilinear form of Lemma 23 . A set of boundary conditions 1B , 4 ̧ ( x ) ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero