## Linear Operators: Spectral theory |

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Page 1290

Nelson Dunford, Jacob T. Schwartz. that since time = ( T271 ) * , the operator i = 0

\ df / is formally self adjoint provided only that the

same way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt

) ...

Nelson Dunford, Jacob T. Schwartz. that since time = ( T271 ) * , the operator i = 0

\ df / is formally self adjoint provided only that the

**coefficients**pi are real . In thesame way , the formal differential operator ( i / 2 ) ( d / dt ) " { p ( t ) ( d / dt ) + ( d / dt

) ...

Page 1435

can be determined by formally substituting the asymptotic expression for o ; in [ *

* ] and comparing

formal differential operator on an interval I having

can be determined by formally substituting the asymptotic expression for o ; in [ *

* ] and comparing

**coefficients**of 2 - " . Thus , in all cases in which we deal with aformal differential operator on an interval I having

**coefficients**analytic in I and ...Page 1730

For partial differential operators in R with

may state the following analogue of the Gårding inequality , Lemma 10 . As to its

proof , we need only remark that since , as has been pointed out above , only ...

For partial differential operators in R with

**coefficients**belonging to COO ( R ) , wemay state the following analogue of the Gårding inequality , Lemma 10 . As to its

proof , we need only remark that since , as has been pointed out above , only ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

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### Common terms and phrases

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 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