## Linear Operators: Spectral theory |

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Page 1310

Then the boundary conditions are real , and there is exactly one solution o ( t , 2 )

of ( 1 - 2 ) = 0

, and exactly one solution y ( t , 2 ) of ( T - 2 ) 4 = 0

Then the boundary conditions are real , and there is exactly one solution o ( t , 2 )

of ( 1 - 2 ) = 0

**square**-**integrable**at a and satisfying the boundary conditions at a, and exactly one solution y ( t , 2 ) of ( T - 2 ) 4 = 0

**square**-**integrable**at b and ...Page 1556

... ( Hartman ) Suppose that the equation tf = 0 has a solution with a finite number

of zeros . Prove that there exists a solution g of the same equation such that g ( t )

- 1 is

... ( Hartman ) Suppose that the equation tf = 0 has a solution with a finite number

of zeros . Prove that there exists a solution g of the same equation such that g ( t )

- 1 is

**square**-**integrable**on a semi - axis sufficiently far removed from the origin .Page 1557

( 2 - 1 ) } = 0 has a solution which is not

T . G20 ( Wintner ) . Suppose that q is bounded below , and suppose that a does

not ...

( 2 - 1 ) } = 0 has a solution which is not

**square**-**integrable**but has a**square**-**integrable**derivative . Prove that the point à belongs to the essential spectrum ofT . G20 ( Wintner ) . Suppose that q is bounded below , and suppose that a does

not ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero