Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 68
Page 1079
... eigenvalues of A ( each eigenvalue repeated a number of times equal to the dimension of the range of E ( ^ ; A ) ) , then the eigenvalues of A ( m ) are his λig ... him 1 , 2 , ... , im being an arbitrary sequence of integers such that ...
... eigenvalues of A ( each eigenvalue repeated a number of times equal to the dimension of the range of E ( ^ ; A ) ) , then the eigenvalues of A ( m ) are his λig ... him 1 , 2 , ... , im being an arbitrary sequence of integers such that ...
Page 1383
... eigenvalues are consequently to be determined from the equation ( cos √λx ) ' | _1 = 0 ; i.e. , from the equation sin √ = 0. Consequently , in Case B , the eigenvalues are the numbers of the form ( nл ) 2 , and the normalized ...
... eigenvalues are consequently to be determined from the equation ( cos √λx ) ' | _1 = 0 ; i.e. , from the equation sin √ = 0. Consequently , in Case B , the eigenvalues are the numbers of the form ( nл ) 2 , and the normalized ...
Page 1497
... eigenvalues which , by Lemma 29 and Corollary 24 , approach plus infinity . By Theorem 64 , we now see that the discrete eigenvalues of those two problems are the only possible end points in the collection of intervals or " bands ...
... eigenvalues which , by Lemma 29 and Corollary 24 , approach plus infinity . By Theorem 64 , we now see that the discrete eigenvalues of those two problems are the only possible end points in the collection of intervals or " bands ...
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