## Linear Operators: Spectral theory |

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Page 1290

is formally self adjoint provided only that the

way, the formal ... Then the leading

is real, while if n is odd, a, is pure imaginary. If n is even, then ti = (d/dt)"/*a,(t) ...

is formally self adjoint provided only that the

**coefficients**p, are real. In the sameway, the formal ... Then the leading

**coefficient**in to is (–1 )"a,; thus, if n is even, anis real, while if n is odd, a, is pure imaginary. If n is even, then ti = (d/dt)"/*a,(t) ...

Page 1435

The

the asymptotic expression for a, ... Thus, in all cases in which we deal with a

formal differential operator on an interval I having

with ...

The

**coefficients**k”, ..., k", e, co, co, ... can be determined by formally substitutingthe asymptotic expression for a, ... Thus, in all cases in which we deal with a

formal differential operator on an interval I having

**coefficients**analytic in I andwith ...

Page 1486

Nelson Dunford, Jacob T. Schwartz. Equations with periodic

are fundamental in the quantum-mechanical theory of solid crystals) have a

number of interesting and important properties. In the next few paragraphs t

denotes a ...

Nelson Dunford, Jacob T. Schwartz. Equations with periodic

**coefficients**(whichare fundamental in the quantum-mechanical theory of solid crystals) have a

number of interesting and important properties. In the next few paragraphs t

denotes a ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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 Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero