## Linear Operators: Spectral theory |

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Page 1162

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

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

with all the maximal ideals of the algebra obtained by adjoining an identity to Ly (

R ) ...

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

**regular**maximalideals of L ( R ) are in one - to - one correspondence with the points of Mo , i . e . ,

with all the maximal ideals of the algebra obtained by adjoining an identity to Ly (

R ) ...

Page 1504

A point zo in the complex plane at which r , and r , are analytic is called a

point of the operator . In the neighborhood of a

unique analytic solution f ( ) of the equation Lf = 0 with specified initial values f (

20 ) ...

A point zo in the complex plane at which r , and r , are analytic is called a

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

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

20 ) ...

Page 1917

( See Reflexivity )

)

( 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 differential ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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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 give 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 remark 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