## Linear Operators: Spectral theory |

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Results 1-3 of 67

Page 1290

that since to ti - (T211)*, the operator X (–) () to () is formally self adjoint provided

only that the

operator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjoint provided that

p(t) is ...

that since to ti - (T211)*, the operator X (–) () to () is formally self adjoint provided

only that the

**coefficients**p, are real. In the same way, the formal differentialoperator (i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjoint provided that

p(t) is ...

Page 1435

by formally substituting the asymptotic expression for a, in [+3] and comparing

operator on an interval I having

end ...

by formally substituting the asymptotic expression for a, in [+3] and comparing

**coefficients**of z-". Thus, in all cases in which we deal with a formal differentialoperator on an interval I having

**coefficients**analytic in I and with poles at the freeend ...

Page 1486

Equations with periodic

mechanical theory of solid crystals) have a number of ... Let t have the form n d j -

3.0 (). and suppose that all the

period.

Equations with periodic

**coefficients**(which are fundamental in the quantum-mechanical theory of solid crystals) have a number of ... Let t have the form n d j -

3.0 (). and suppose that all the

**coefficients**a, are periodic and have the sameperiod.

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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