## Linear Operators: Spectral theory |

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Page 1270

The

adjoint extension is of crucial importance in determining whether the spectral

theorem may be employed . If the answer to this

important to ...

The

**problem**of determining whether a given symmetric operator has a selfadjoint extension is of crucial importance in determining whether the spectral

theorem may be employed . If the answer to this

**problem**is affirmative , it isimportant to ...

Page 1630

Then we may say that the Cauchy

set go , 81 , . . . , & m - 1 of infinitely differentiable functions defined on s , there

exists a unique function f in Co ( D ) , satisfying the equation Lf = 0 , and such that

...

Then we may say that the Cauchy

**problem**for L consists in showing that for eachset go , 81 , . . . , & m - 1 of infinitely differentiable functions defined on s , there

exists a unique function f in Co ( D ) , satisfying the equation Lf = 0 , and such that

...

Page 1831

Sur une généralisation du théorème de Plancherel au cas des intégrales de

Fourier sur les groupes topologiques commutatifs . Doklady Akad . Nauk SSSR (

N . S . ) 30 , 484 - 488 ( 1941 ) . Infinite J - matrices and a matrix moment

.

Sur une généralisation du théorème de Plancherel au cas des intégrales de

Fourier sur les groupes topologiques commutatifs . Doklady Akad . Nauk SSSR (

N . S . ) 30 , 484 - 488 ( 1941 ) . Infinite J - matrices and a matrix moment

**problem**.

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero