## Linear Operators: Spectral theory |

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Page 1310

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

of a separated symmetric set of boundary conditions. Let Jož # 0. Then the

boundary conditions are real, and there is ea actly one

0 ...

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

of a separated symmetric set of boundary conditions. Let Jož # 0. Then the

boundary conditions are real, and there is ea actly one

**solution**p(t, A) of (t–A) p =0 ...

Page 1464

Then (a) if lim sup, ... tog(t) < —(1/4), every

number of zeros on [a, oo); (b) if lim inf, .<!”q(t) > —(1/4), no

identically zero, of ts = 0 has more than a finite number of zeros on [a, oo). PRoof.

According to ...

Then (a) if lim sup, ... tog(t) < —(1/4), every

**solution**of ts = 0 has an infinitenumber of zeros on [a, oo); (b) if lim inf, .<!”q(t) > —(1/4), no

**solution**, notidentically zero, of ts = 0 has more than a finite number of zeros on [a, oo). PRoof.

According to ...

Page 1521

Putting yo = 1/2+i so that Žo = 1 +i, we see that the equation (L1–Åo)f has one

ob. The

has ...

Putting yo = 1/2+i so that Žo = 1 +i, we see that the equation (L1–Åo)f has one

**solution**of the order of to "To as t → 00 and another which behaves like to as t →ob. The

**solution**at 20 = 1–i is exactly similar. Thus, by Theorem XII.4.19, L1–2has ...

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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