## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

### From inside the book

Results 1-3 of 66

Page 1217

Two ordered representations U and Ở of H relative to T and †

Two ordered representations U and Ở of H relative to T and †

**respectively**, with measures u and ù , and multiplicity sets { en } and { ēn } will be called equivalent if u zû and ule , 4ěn ) = 0 = ūle 4ěn ) for n = 1 , 2 , .Page 1326

for all solutions of ( 1-2 ) 0 = 0 ( ( 7 * —ā ) 0 = 0 ) which are squareintegrable in a neighborhood of a and b

for all solutions of ( 1-2 ) 0 = 0 ( ( 7 * —ā ) 0 = 0 ) which are squareintegrable in a neighborhood of a and b

**respectively**, and which satisfy the boundary conditions at a and at b**respectively**. Then the resolvent R ( 2 ; T ) = ( 21 ...Page 1548

extensions of S and Ŝ

extensions of S and Ŝ

**respectively**, and let 2n ( T ) and an ( Î ) be the numbers defined for the self adjoint operators T and Î as in Exercise D2 . Show that an ( T ) 22n ( † ) , n 2 1 . D11 Let T , be a self adjoint operator in ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero