## Linear Operators: Spectral theory |

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Page 1250

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

Lemma 1.6(c), AP* = To. Hence T^T = AP*PA. Since, by Lemma 5, Po P is a

projection onto SR(A), it follows that T*T = A*. The uniqueness of A now follows

from ...

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

**unique**. ByLemma 1.6(c), AP* = To. Hence T^T = AP*PA. Since, by Lemma 5, Po P is a

projection onto SR(A), it follows that T*T = A*. The uniqueness of A now follows

from ...

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 | |

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