## Linear Operators: Spectral theory |

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Page 1280

It is nearly evident that the topology for C"(I) is independent of the particular

sequence {J} of compact subintervals of I used in its definition. 1 DEFINITION. A

It is nearly evident that the topology for C"(I) is independent of the particular

sequence {J} of compact subintervals of I used in its definition. 1 DEFINITION. A

**formal differential operator**of order n on the interval I is an expression t = a, (t) ...Page 1289

Q.E.D. A number of other principles belonging to the formal algebra of

of them; for this reason they will not be numbered as theorems and lemmas.

Q.E.D. A number of other principles belonging to the formal algebra of

**formal****differential operators**are worth mentioning although we shall not make much useof them; for this reason they will not be numbered as theorems and lemmas.

Page 1290

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

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 differential****operator**(i/2)(d/dt)"{p(t)(d/dt)+(d/dt)p(t)}(d/dt)" is formally self adjoint provided thatp(t) is ...

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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