## Linear Operators: Spectral theory |

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Page 1310

shall show the theorem is true in each of the four cases discussed above. In case

(iv), since there are no boundary values, no boundary conditions are imposed; ...

**square**-**integrable**at b and satisfying the boundary conditions at b. PROOF. Weshall show the theorem is true in each of the four cases discussed above. In case

(iv), since there are no boundary values, no boundary conditions are imposed; ...

Page 1556

G16 (Hartman) Suppose that the equation ts = 0 has a solution with a finite

number of zeros. Prove that there exists a solution g of the same equation such

that g(t)-" is

origin.

G16 (Hartman) Suppose that the equation ts = 0 has a solution with a finite

number of zeros. Prove that there exists a solution g of the same equation such

that g(t)-" is

**square**-**integrable**on a semi-axis sufficiently far removed from theorigin.

Page 1557

(A–t)f = 0 has a solution which is not

G20 (Wintner). Suppose that q is bounded below, and suppose that A does not

belong ...

(A–t)f = 0 has a solution which is not

**square**-**integrable**but has a**square**-**integrable**derivative. Prove that the point A belongs to the essential spectrum of t.G20 (Wintner). Suppose that q is bounded below, and suppose that A does not

belong ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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