## Linear Operators: Spectral theory |

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Page 937

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

mathematics.

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

**theory**of normal operators to problems in a variety of fields ofmathematics.

Page 1435

Thus, in all cases in which we deal with a formal differential operator on an

interval I having coefficients analytic in I and with poles at the free end points of I,

the

of ...

Thus, in all cases in which we deal with a formal differential operator on an

interval I having coefficients analytic in I and with poles at the free end points of I,

the

**theory**of regular and irregular singularities enables us to reduce the problemof ...

Page 1645

Hence, we are led to the attempt to define some sort of “generalized function.” A

very complete and interesting development of such a

functions was given by Laurent Schwartz; the generalized functions were called

by ...

Hence, we are led to the attempt to define some sort of “generalized function.” A

very complete and interesting development of such a

**theory**of generalizedfunctions was given by Laurent Schwartz; the generalized functions were called

by ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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 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 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