Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 93
Page 949
... seen ( Theorem 2 ) that AP is isometric and isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma 3 ) that the con- tinuous characters of S are of the form ei . By Theorem 1.6 , the set of continuous characters ...
... seen ( Theorem 2 ) that AP is isometric and isomorphic with C ( S ) , where S is a compact Abelian group , and also ( Lemma 3 ) that the con- tinuous characters of S are of the form ei . By Theorem 1.6 , the set of continuous characters ...
Page 1154
... seen from Corollary III.11.6 , is a consequence of the assertion that ( ii ) ; ( 2 ) ( 4xB ) = cλ ( A ) 2 ( B ) , Α , Β Ε Σ . Thus we shall endeavor to establish ( ii ) . For every E in Σ ( 2 ) let μ ( E ) = 2 ( 2 ) ( hE ) where h is ...
... seen from Corollary III.11.6 , is a consequence of the assertion that ( ii ) ; ( 2 ) ( 4xB ) = cλ ( A ) 2 ( B ) , Α , Β Ε Σ . Thus we shall endeavor to establish ( ii ) . For every E in Σ ( 2 ) let μ ( E ) = 2 ( 2 ) ( hE ) where h is ...
Page 1324
... seen ( cf. Theorem 10 ) that ta ; 0 , 1 , ... , n . Thus choosing a basis { } , i i - - 1 , ... , n , for the solutions of tσ = 0 , and defining the matrix { T } by the equations τσ n - Σ Γυξη , i = . 1. . , n , j = 1 the jump equations ...
... seen ( cf. Theorem 10 ) that ta ; 0 , 1 , ... , n . Thus choosing a basis { } , i i - - 1 , ... , n , for the solutions of tσ = 0 , and defining the matrix { T } by the equations τσ n - Σ Γυξη , i = . 1. . , n , j = 1 the jump equations ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
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