## Linear Operators: Spectral theory |

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Page 1310

Then the boundary conditions are real, and there is eractly one

(r—A) p = 0 square-integrable at a and satisfying the boundary conditions at a,

and exactly one

...

Then the boundary conditions are real, and there is eractly one

**solution**p(t, A) of(r—A) p = 0 square-integrable at a and satisfying the boundary conditions at a,

and exactly one

**solution**p(t, A) of (t–A) p = 0 square-integrable at b and satisfying...

Page 1472

least one such

to - Ao satisfy B. By the remark (a) made above, it then follows that for any two ...

least one such

**solution**must exist. On the other hand, if two linearly independent**solutions**of to - Ao satisfy the boundary condition B, it follows that all**solutions**ofto - Ao satisfy B. By the remark (a) made above, it then follows that for any two ...

Page 1632

and imaginary parts of a

]|a's P 0} are the real parts of a pair of analytic functions of the complex variable z

= a1-i-ia's defined in that region. Hence, a

and imaginary parts of a

**solution**of the equation Vof = 0 in the region R = {[a'i, as]|a's P 0} are the real parts of a pair of analytic functions of the complex variable z

= a1-i-ia's defined in that region. Hence, a

**solution**of W*f = 0 in R is an analytic ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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