## Linear Operators: Spectral theory |

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= 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, (a) = 0, j = 1,..., m, is said to be stronger than the set B, (a)= 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 ...Page 1305

If B(f) = 0 is not a

the equation B(f) = 0 may be written as Bi(f) = B2(f), ... A 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) = B2(f), ... A set of

**boundary****conditions**is said to be separated if it (or, more generally, some set of**boundary****conditions**...Page 1310

imposition of a separated symmetric set of

Then the

(r—A) p = 0 square-integrable at a and satisfying the

and ...

imposition of a separated symmetric set of

**boundary conditions**. Let JAA # 0.Then the

**boundary conditions**are real, and there is eractly one solution p(t, A) of(r—A) p = 0 square-integrable at a and satisfying the

**boundary conditions**at a,and ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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