Linear Operators: Spectral theory |
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Page 1191
... operator is not self adjoint for it is clear from the above equations that any function g with a continuous first ... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given ...
... operator is not self adjoint for it is clear from the above equations that any function g with a continuous first ... adjoint of id / dt . The problem , suggested by the preceding example , of finding self adjoint extensions of a given ...
Page 1270
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
... operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed . If the answer to this problem is affirmative , it is important to know what the self adjoint extensions look ...
Page 1548
... adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in H 12 by setting D ( T ) = D ( T1 ) → D ( T1⁄2 ) and 2 - Tx = T ( x1x2 ) = T11 → TqX2 , Ꮎ x = D ( T ) . Show that ...
... adjoint operator in Hilbert space 1 , and let T2 be a self adjoint operator in Hilbert space 2. Define the operator T in H 12 by setting D ( T ) = D ( T1 ) → D ( T1⁄2 ) and 2 - Tx = T ( x1x2 ) = T11 → TqX2 , Ꮎ x = D ( T ) . Show that ...
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