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 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 ...
Page 1591
... given in Theorem 4. The development followed in this section and the next , which makes extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naimark [ 5 ] . A version of Lemma 7 is due to Glazman [ 1 , 2 ] . A result ...
... given in Theorem 4. The development followed in this section and the next , which makes extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naimark [ 5 ] . A version of Lemma 7 is due to Glazman [ 1 , 2 ] . A result ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero