## 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, William G. Bade, Robert G. Bartle. Equations

with periodic

theory of solid crystals) have a number of interesting and important properties.

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Equations

with periodic

**coefficients**(which are fundamental in the quantum-mechanicaltheory of solid crystals) have a number of interesting and important properties.

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad 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 singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero