## Linear Operators: Spectral theory |

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Page 1310

Then the boundary conditions are real, and there is eractly one solution p(t, A) of

(r—A) p = 0

and exactly one solution p(t, A) of (t–A) p = 0

...

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 1329

Then the boundary conditions are real, and there is exactly one solution p(t, A) of

(t–A)0 = 0

ea actly one solution p(t, 2) of (t—A)0 = 0

Then the boundary conditions are real, and there is exactly one solution p(t, A) of

(t–A)0 = 0

**square**-**integrable**at a and satisfying the boundary conditions at a, andea actly one solution p(t, 2) of (t—A)0 = 0

**squareintegrable**at b satisfying the ...Page 1552

Prove that the equation rj = 0 has a

Suppose that the operator r has the property that whenever f is a

Prove that r ...

Prove that the equation rj = 0 has a

**square**-**integrable**solution. G2 (Wintner)Suppose that the operator r has the property that whenever f is a

**square**-**integrable**solution of the equation (2–1)f = 0, then f is also**square**-**integrable**. (a)Prove that r ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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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