## 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 1622

1 + I . The converse

differential operators to a variety of

shown a physical meaning for many of the mathematical notions , but has also

raised ...

1 + I . The converse

**problem**. The wide application of the spectral theory ofdifferential operators to a variety of

**problems**in modern physics not only hasshown a physical meaning for many of the mathematical notions , but has also

raised ...

Page 1703

The Elliptic Boundary Value

spectral theory of Chapter XIII be generalized to partial differential operators ? In

the present section it will be seen that it can , at least for the class of elliptic partial

...

The Elliptic Boundary Value

**Problem**Can the boundary value theory and thespectral theory of Chapter XIII be generalized to partial differential operators ? In

the present section it will be seen that it can , at least for the class of elliptic partial

...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero