## Linear Operators: Spectral theory |

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Page 1162

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

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) ...

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

**regular**maximalideals 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 1504

A point zo in the complex plane at which ri and r2 are analytic is called a

point of the operator. In the neighborhood of a

unique analytic solution f(z) of the equation Lj = 0 with specified initial values f(zo

), ...

A point zo in the complex plane at which ri and r2 are analytic is called a

**regular**point of the operator. In the neighborhood of a

**regular**point zo, there exists aunique analytic solution f(z) of the equation Lj = 0 with specified initial values f(zo

), ...

Page 1917

(See Reflexivity)

equation, XIII.6 ...

(See Reflexivity)

**Regular**closure, (462–463)**Regular**convexity, (462–463)**Regular**element in a B-algebra, IX.1.2 (861)**Regular**element in a ring, (40)**Regular**method of summability, II.4.35 (75)**Regular**point of a differentialequation, XIII.6 ...

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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