Linear Operators: Spectral theory |
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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 A ,, ... , A , be a complete set of boundary values for T , and let Σo ̧¡ ± ‚ ¤¡¡Â¿Ã ̧ be the bilinear form of Lemma 23 . A set of boundary conditions B1 , 4 , ( x ) ...
... symmetric operator with finite deficiency indices whose sum is p . Let A ,, ... , A , be a complete set of boundary values for T , and let Σo ̧¡ ± ‚ ¤¡¡Â¿Ã ̧ be the bilinear form of Lemma 23 . A set of boundary conditions B1 , 4 , ( x ) ...
Page 1272
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero