## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1310

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

of ( T - 219 = 0

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

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

of ( T - 219 = 0

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

**square**-**integrable**at b and ...Page 1329

Let In +0 . Then the boundary conditions are real , and there is exactly one

solution q ( t , 2 ) of ( 1-2 ) = 0

conditions at a , and exactly one solution y ( t , 2 ) of ( T - 1 ) 0 = 0

Let In +0 . Then the boundary conditions are real , and there is exactly one

solution q ( t , 2 ) of ( 1-2 ) = 0

**square**-**integrable**at a and satisfying the boundaryconditions at a , and exactly one solution y ( t , 2 ) of ( T - 1 ) 0 = 0

**squareintegrable**at ...Page 1416

( b ) By Theorem 11 , it will suffice to show that every solution of the equation to =

0 is

solution of the equation [ ** o ' - kt - 20 ( 0 < k < 1 ) . Let ta be subjected to the

boundary ...

( b ) By Theorem 11 , it will suffice to show that every solution of the equation to =

0 is

**square**-**integrable**. Let | be a real solution of this equation . Let t2 be asolution of the equation [ ** o ' - kt - 20 ( 0 < k < 1 ) . Let ta be subjected to the

boundary ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 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 Nauk 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