## Linear Operators: Spectral theory |

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Page 1381

By the

+ f ( 1 ) form a complete set of boundary values for t , and the most general self

adjoint extension To of To ( t ) is defined by a boundary condition f ( 0 ) = ei°f ( 1 )

.

By the

**remark**following Definition 2 . 29 , the two linear functionals f + f ( 0 ) and |+ f ( 1 ) form a complete set of boundary values for t , and the most general self

adjoint extension To of To ( t ) is defined by a boundary condition f ( 0 ) = ei°f ( 1 )

.

Page 1472

On the other hand , if two linearly independent solutions of to = lo satisfy the

boundary condition B , it follows that all solutions of to = ho satisfy B . By the

and a < c ...

On the other hand , if two linearly independent solutions of to = lo satisfy the

boundary condition B , it follows that all solutions of to = ho satisfy B . By the

**remark**( a ) made above , it then follows that for any two solutions f , g of to = 2o ,and a < c ...

Page 1900

15 (379) definition, IV.2.25 (242)

Almost uniform (or ^-uniform convergence) definition, III. 6.1(145). (See also

Convergence of functions) Analytic continuation, (230) Analytic function (vector-

valued) ...

15 (379) definition, IV.2.25 (242)

**remarks**concerning, (386-387) study of, IV.7Almost uniform (or ^-uniform convergence) definition, III. 6.1(145). (See also

Convergence of functions) Analytic continuation, (230) Analytic function (vector-

valued) ...

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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