## Linear Operators: Spectral theory |

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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 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

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