## Linear Operators: Spectral operators |

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Page 2351

Approximation by Generalized

spectrum of a discrete spectral operator T is distributed in the complex plane in

too chaotic a way for the very restrictive hypothesis of Theorem 2 . 7 to apply , a

variant ...

Approximation by Generalized

**Eigenfunctions**In many cases in which thespectrum of a discrete spectral operator T is distributed in the complex plane in

too chaotic a way for the very restrictive hypothesis of Theorem 2 . 7 to apply , a

variant ...

Page 2374

function in terms of

operator has been discussed by many authors . In addition , it is desirable to

know when the ...

**EIGENFUNCTION**EXPANSIONS . The question of the expansion of a givenfunction in terms of

**eigenfunctions**( or generalized**eigenfunctions**) of anoperator has been discussed by many authors . In addition , it is desirable to

know when the ...

Page 2538

Orthogonality of the

Arch . Rat . Mech . Anal . 19 , 71 - 73 ( 1965 ) . 4 . On the

connected with the exterior problem for the Schrödinger equation . Japanese J ...

Orthogonality of the

**eigenfunctions**for the exterior problem connected with - 4 .Arch . Rat . Mech . Anal . 19 , 71 - 73 ( 1965 ) . 4 . On the

**eigenfunction**expansionconnected with the exterior problem for the Schrödinger equation . Japanese J ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero