## Linear Operators: Spectral theory |

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Page 1236

0, i = 1,..., k, if the boundary values B, are all linear combinations of the C, . If each

of two sets of

**boundary conditions**C,(r) = 0, j = 1,..., m, is said to be stronger than the set B,(r) =0, i = 1,..., k, if the boundary values B, are all linear combinations of the C, . If each

of two sets of

**boundary conditions**is stronger than the other, then the sets are ...Page 1305

If B(f) = 0 is not a

the equation B(f) = 0 may be written as Bi(f) = B.(f), ... A set of

is said to be separated if it (or, more generally, some set of

If B(f) = 0 is not a

**boundary condition**either at a or at b (so that, by Theorem 19,the equation B(f) = 0 may be written as Bi(f) = B.(f), ... A set of

**boundary conditions**is said to be separated if it (or, more generally, some set of

**boundary conditions**...Page 1310

... G. Bade, Robert G. Bartle. imposition of a separated symmetric set of

actly one solution p(t, A) of (t–A) p = 0 square-integrable at a and satisfying the ...

... 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 eaactly one solution p(t, A) of (t–A) p = 0 square-integrable at a and satisfying the ...

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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