## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 82

Page 1126

of the closed set C ; we shall

( C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

of the closed set C ; we shall

**denote**this subspace of L2 [ 0 , 1 ] by the symbol L2( C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

Page 1486

In the next few paragraphs t

operator of order n , defined on the interval R = { - 00 < i < too } . Let t have the

form m idii = , 441 ( ) ' . and suppose that all the coefficients a ; are periodic and

have ...

In the next few paragraphs t

**denotes**a formally self adjoint formal differentialoperator of order n , defined on the interval R = { - 00 < i < too } . Let t have the

form m idii = , 441 ( ) ' . and suppose that all the coefficients a ; are periodic and

have ...

Page 1636

In general , unless the contrary is explicitly stated , J , I , J , etc . , will

indices for E " , that is , indices whose range of variation is restricted by the

condition min J 21 , max J S n . The symbols J , , , , , will similarly

for En + 1 .

In general , unless the contrary is explicitly stated , J , I , J , etc . , will

**denote**indices for E " , that is , indices whose range of variation is restricted by the

condition min J 21 , max J S n . The symbols J , , , , , will similarly

**denote**indicesfor En + 1 .

### What people are saying - Write a review

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

### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

### Common terms and phrases

additive 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 differential equations domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem Proc projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero