## Linear Operators: Spectral theory |

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Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract “

see that the discussion leads us to a number of results about deficiency indices.

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract “

**boundary values**” introduced in the last chapter. We shallsee that the discussion leads us to a number of results about deficiency indices.

Page 1298

If t is formally self adjoint, then Definition 17 of a

with Definition XII.4.20 of a

theorem gives a basic property of

the ...

If t is formally self adjoint, then Definition 17 of a

**boundary value**for t coincideswith Definition XII.4.20 of a

**boundary value**for To(t). PRoof. ... Q.E.D. The nexttheorem gives a basic property of

**boundary values**of differential operators. Forthe ...

Page 1307

D, are

)|D2(g)–D2(f)|D1(g), f, ge Q(T(r)). PRoof. Let A be any

**boundary values**C1, C2, D1, D2 where C1, C2 are**boundary values**at a and D1,D, are

**boundary values**at b, such that (rf, g)–(f, rg) = C1(f)C2(g)–C2(f)C1(g) +D1(f)|D2(g)–D2(f)|D1(g), f, ge Q(T(r)). PRoof. Let A be any

**boundary value**for t.### What people are saying - Write a review

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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