## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 66

Page 1079

Show that if an , ... , in are

number of times equal to the dimension of the range of E ( ; A ) ) , then the

integers ...

Show that if an , ... , in are

**eigenvalues**of A ( each**eigenvalue**à being repeated anumber of times equal to the dimension of the range of E ( ; A ) ) , then the

**eigenvalues**of A ( m ) are din his ij , ig , ... , im being an arbitrary sequence ofintegers ...

Page 1383

With boundary conditions A , the

from the equation sin vā = 0 . Consequently , in Case A , the

numbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } " , n 2 0.

With boundary conditions A , the

**eigenvalues**are consequently to be determinedfrom the equation sin vā = 0 . Consequently , in Case A , the

**eigenvalues**are thenumbers of the form ( na ) , n 2 1 ; in Case C , the numbers { ( n + ] ) a } " , n 2 0.

Page 1497

In the former case the matrix B ( A ) necessarily has an eigenvector belonging to

the

self adjoint operators T , and T , whose spectra consist entirely of

In the former case the matrix B ( A ) necessarily has an eigenvector belonging to

the

**eigenvalue**+1 ; in the latter case , to ... sets of boundary conditions determineself adjoint operators T , and T , whose spectra consist entirely of

**eigenvalues**...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero