Linear Operators: Spectral theory |
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Page 884
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
... given here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in greater generality . A simple direct proof of Corollary 3.6 was given by Fukamiya [ 2 ] , and can be used to prove Lemma 3.5 . Corollary 3.10 ...
Page 909
... given by the formula ( F ( T ) x ) ( 2 ) = F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a ...
... given by the formula ( F ( T ) x ) ( 2 ) = F ( 2 ) x ( 2 ) . Our first purpose in this section is to show that , in a sense , the example just given is typical of the structure of every normal operator . More explicitly , if T is a ...
Page 1149
... given in Weyl's memoir Theorie der Darstellungen kontinuierlicher halb - einfachen Gruppen durch lineare Transformationen III , Math . Zeitschift v . 24 ( 1926 ) p . 377-395 . The representation theory for groups which are neither ...
... given in Weyl's memoir Theorie der Darstellungen kontinuierlicher halb - einfachen Gruppen durch lineare Transformationen III , Math . Zeitschift v . 24 ( 1926 ) p . 377-395 . The representation theory for groups which are neither ...
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