## Linear Operators: Spectral theory |

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Page 1301

... immediately from the preceding corollary. Q.E.D. 25 CoRollary. Let t be a

formally self adjoint formal differential operator of order n defined on an interval I

with end points a and b. Let a < c < b, and let t' and t” be

restrictions of ...

... immediately from the preceding corollary. Q.E.D. 25 CoRollary. Let t be a

formally self adjoint formal differential operator of order n defined on an interval I

with end points a and b. Let a < c < b, and let t' and t” be

**respectively**therestrictions of ...

Page 1302

Corollary 23 and from Theorems 19 and 20 that d' and d" exceed by n the

number of independent boundary values at a and at b

statement of the present corollary is then evident. Q.E.D. 26 CoRollARY. (Kodaira

) Under the ...

Corollary 23 and from Theorems 19 and 20 that d' and d" exceed by n the

number of independent boundary values at a and at b

**respectively**. Thestatement of the present corollary is then evident. Q.E.D. 26 CoRollARY. (Kodaira

) Under the ...

Page 1326

for all solutions of (r—A)0 = 0 ((t” –7)0 = 0) which are squareintegrable in a

neighborhood of a and b

at a and at b

...

for all solutions of (r—A)0 = 0 ((t” –7)0 = 0) which are squareintegrable in a

neighborhood of a and b

**respectively**, and which satisfy the boundary conditionsat a and at b

**respectively**. Then the resolvent R(A; T) = (AI–T)-1 is given by the ea...

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### Contents

SPECTRAL THEORY | 858 |

868 | 885 |

Miscellaneous Applications | 937 |

Copyright | |

38 other sections not shown

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix 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