## Linear Operators: Spectral theory |

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Results 1-3 of 87

Page 1250

Finally we show that the decomposition T = PA of the theorem is

Lemma ... Since A is

P(Aa) = Tr. Further the extension of P by continuity from SR(A) to R(A) is

Finally we show that the decomposition T = PA of the theorem is

**unique**. ByLemma ... Since A is

**unique**, P is**uniquely**determined on R(A) by the equation ofP(Aa) = Tr. Further the extension of P by continuity from SR(A) to R(A) is

**unique**.Page 1283

Thus, equation (e') has the

–1) to H. j=0 Since all the terms in equation (e) but the first are absolutely

continuous, it follows that F is absolutely continuous. Thus Theorem 1 is proved

for the ...

Thus, equation (e') has the

**unique**solution (cf. Lemma VII.3.4) F = (1+q)-1H = X (–1) to H. j=0 Since all the terms in equation (e) but the first are absolutely

continuous, it follows that F is absolutely continuous. Thus Theorem 1 is proved

for the ...

Page 1383

With boundary conditions A and C, the

boundary condition raq = Mo is sin Våt. With boundary conditions A, the

eigenvalues are consequently to be determined from the equation sin V2 = 0.

With boundary conditions A and C, the

**unique**solution of tso = Ao satisfying theboundary condition raq = Mo is sin Våt. With boundary conditions A, the

eigenvalues are consequently to be determined from the equation sin V2 = 0.

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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