## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2434

... of an interesting class of

... of an interesting class of

**partial**differential operators . 22 THEOREM . Let n be an integer 23 , and let En be the real n - dimensional Euclidean space . ( a ) Let 7 be the formal**partial**differential operator 02 22 ( 1 ) + + Ox ...Page 2516

**Partial**Diff . Equations ( Novosibirsk , 1963 ) , pp . 26–32 . Acad . Sci . USSR Siberian Branch , Moscow , 1963 . 5. Expansions in eigenfunctions of self - adjoint operators . Amer . Math . Soc . Transl . of Math .Page 2534

Eigenfunction expansions and scattering theory for perturbed elliptic

Eigenfunction expansions and scattering theory for perturbed elliptic

**partial**differential operators . Bull . Amer . Math . Soc . 70 , 517–521 ( 1964 ) . Grothendieck , A. 3 . Produits tensoriels topologiques et espaces nucléaires .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

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