## Linear Operators: Spectral theory |

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Page 1187

Just as in the case of a bounded operator the

is defined to be the set of all complex numbers a such that ( 21 - T ) -1 exists as

an everywhere defined bounded operator . For å in p ( T ) the symbol R ( 2 ; T ) ...

Just as in the case of a bounded operator the

**resolvent**set p ( T ) of an operator Tis defined to be the set of all complex numbers a such that ( 21 - T ) -1 exists as

an everywhere defined bounded operator . For å in p ( T ) the symbol R ( 2 ; T ) ...

Page 1330

Spectral Theory : Compact

formally self adjoint formal differential ... present section will be devoted to the

spectral theory of such extensions T in the important special case in which the

Spectral Theory : Compact

**Resolvents**We saw in Section 2 that with eachformally self adjoint formal differential ... present section will be devoted to the

spectral theory of such extensions T in the important special case in which the

**resolvent**R ...Page 1422

Thus , from [ 71 ] is follows that -i is in the

real number such that the whole interval [ -i , -Mol ) of the negative imaginary axis

is in the

Thus , from [ 71 ] is follows that -i is in the

**resolvent**set of S. Let Mo be the largestreal number such that the whole interval [ -i , -Mol ) of the negative imaginary axis

is in the

**resolvent**set of S. Since , by Lemma XII.1.3 , the**resolvent**set is open ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic 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 derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk 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