## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1027

Suppose that 1 + 0

Suppose that 1 + 0

**belongs**to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that 2 is an eigenvalue and hence for some non - zero x in H we have Tx = ax , and hence , since T = TE , we have ( ET ) ( Ex ) = 1 Ex . Hence i ...Page 1116

Then plainly = Σ Βφ . / 2 = Σ ( γP / 2 52 < α , 42 ** < = i = 1 ܕ so that , by Definition 6.1 , B

Then plainly = Σ Βφ . / 2 = Σ ( γP / 2 52 < α , 42 ** < = i = 1 ܕ so that , by Definition 6.1 , B

**belongs**to the Hilbert - Schmidt class Cz . If we let Aq ; = y -p / 2 Pi , then A is plainly self adjoint and A**belongs**2 to the class Co ...Page 1602

( 47 ) In ( 0 , 0 ) , suppose that the equation ( 2-1 ) } = 0 has two linearly independent solutions f and g such that Só ' 11 " ( s ) ? ds = 016 ) 0 ( ta and Solg ' ( s ) / ? ds = 0 ( 1 ) Then the point 2

( 47 ) In ( 0 , 0 ) , suppose that the equation ( 2-1 ) } = 0 has two linearly independent solutions f and g such that Só ' 11 " ( s ) ? ds = 016 ) 0 ( ta and Solg ' ( s ) / ? ds = 0 ( 1 ) Then the point 2

**belongs**to the essential ...### What people are saying - Write a review

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

### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

Copyright | |

44 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero