## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2051

We next consider a different type of

and given by the formal differential operator defined on 02 by the matrix ( 112 ) A

22 D2 Baa 202 where ß # 0 is a complex constant , a a = dot oli + a + αN an as1 ...

We next consider a different type of

**perturbed**Laplacian with p = 2 , N arbitrary ,and given by the formal differential operator defined on 02 by the matrix ( 112 ) A

22 D2 Baa 202 where ß # 0 is a complex constant , a a = dot oli + a + αN an as1 ...

Page 2334

The eigenvalues of T have the asymptotic distribution as stated in Lemma 4 . We

now turn to consider the case in which n is odd . Case 2 : n odd . n Let n = 2v + 1.

Let wj , 2334 XIX.4.8 XIX .

The eigenvalues of T have the asymptotic distribution as stated in Lemma 4 . We

now turn to consider the case in which n is odd . Case 2 : n odd . n Let n = 2v + 1.

Let wj , 2334 XIX.4.8 XIX .

**PERTURBATIONS**OF SPECTRAL OPERATORS.Page 2528

Finite dimensional

270 ( 1960 ) . 7. Computations of the multiplicity function . Pacific J. Math . 10 ,

539-546 ( 1960 ) . 8. On a paper of A. Feldzamen . Israel J. Math . 1 , 133–138 (

1963 ) ...

Finite dimensional

**perturbations**in Banach spaces . Amer . J. Math . 82 , 260_270 ( 1960 ) . 7. Computations of the multiplicity function . Pacific J. Math . 10 ,

539-546 ( 1960 ) . 8. On a paper of A. Feldzamen . Israel J. Math . 1 , 133–138 (

1963 ) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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 defined Definition denote dense determined differential operator discrete 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