## Linear Operators: Spectral theory |

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Results 1-3 of 82

Page 1550

E8 ( Bellman ) Suppose that every solution of the equation tt = 0 is of class L ( I )

and that every solution of the equation 7 * 4 = 0 is of class Lq ( I ) ( p - 1 + q - 1 = 1

) ...

**Prove**that the essential spectrum of the operator 7 in L , ( I ) is the empty set . . :E8 ( Bellman ) Suppose that every solution of the equation tt = 0 is of class L ( I )

and that every solution of the equation 7 * 4 = 0 is of class Lq ( I ) ( p - 1 + q - 1 = 1

) ...

Page 1557

Suppose that q is bounded below , and suppose that à does not belong to the

essential spectrum of t . Let f be a square - integrable solution of the equation ( 2 -

1 ) ...

**Prove**that the point 2 belongs to the essential spectrum of t . G20 ( Wintner ) .Suppose that q is bounded below , and suppose that à does not belong to the

essential spectrum of t . Let f be a square - integrable solution of the equation ( 2 -

1 ) ...

Page 1568

if Soot / g ( t ) | dt 21 . H13 Suppose that Soo ( 1 + t ) [ g ( t ) \ dt < c .

origin lies in the continuous spectrum of every self adjoint extension of the ...

**Prove**that a self adjoint extension of the operator has a negative eigenvalue onlyif Soot / g ( t ) | dt 21 . H13 Suppose that Soo ( 1 + t ) [ g ( t ) \ dt < c .

**Prove**that theorigin lies in the continuous spectrum of every self adjoint extension of the ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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