## Linear Operators: Spectral theory |

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Page 1162

is isomorphic with the complex field, and it turns out that the regular maximal

ideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra

is isomorphic with the complex field, and it turns out that the regular maximal

ideals of L1(R) are in one-to-one correspondence with the points of .40, i.e., with

all the maximal ideals of the algebra

**obtained**by adjoining an identity to L1(R) ...Page 1318

Suppose that the homogeneous system

non-trivial solution osc), £(c), and let Kos.) be the function (of the variable s)

Suppose that the homogeneous system

**obtained**from equations [1] and [2] has anon-trivial solution osc), £(c), and let Kos.) be the function (of the variable s)

**obtained**by substituting 2% and Bo for 2, and B, in [f]. The function Ko is ...Page 1624

In the same way, the functions costv/7

property s. cos svä costv/Au(d2) = 0, s # t. ... Their first step consists in

an expression for f(t, A) as a “linear combination” of the functions costv/7 in terms

of ...

In the same way, the functions costv/7

**obtained**from the operator ro enjoy theproperty s. cos svä costv/Au(d2) = 0, s # t. ... Their first step consists in

**obtaining**an expression for f(t, A) as a “linear combination” of the functions costv/7 in terms

of ...

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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