## Linear Operators: Spectral theory |

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Results 1-3 of 59

Page 1290

that since to ti - (T211)*, the operator X (–) () to () is

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

p(t) is ...

that since to ti - (T211)*, the operator X (–) () to () is

**formally self adjoint**providedonly 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 ...

Page 1295

If the (regular or irregular) formal differential operator t is

the operator To(r) is symmetric. PRoof. Clearly To(r) C Ti(t). Corollary 5 shows

that Ti(r) C To(t)*. Q.E.D. We recall (cf. Definition XII.4.9) that if t is formally self ...

If the (regular or irregular) formal differential operator t is

**formally self adjoint**thenthe operator To(r) is symmetric. PRoof. Clearly To(r) C Ti(t). Corollary 5 shows

that Ti(r) C To(t)*. Q.E.D. We recall (cf. Definition XII.4.9) that if t is formally self ...

Page 1464

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. be a real,

Then (a) if lim sup, ... tog(t) < —(1/4), every solution of ts = 0 has an infinite

number ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. be a real,

**formally self adjoint**formal differential operator defined on an interval [a, oo).Then (a) if lim sup, ... tog(t) < —(1/4), every solution of ts = 0 has an infinite

number ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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