## Linear Operators: Spectral theory |

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Page 1433

Nelson Dunford, Jacob T. Schwartz. is called the indicial

the indicial

integer, then the set of solutions of [*] has a basis of the form o,(z) = 2*p,(z), where

p, ...

Nelson Dunford, Jacob T. Schwartz. is called the indicial

**equation**of [+] at zero. Ifthe indicial

**equation**has distinct roots ei, ..., ea, no two of which differ by aninteger, then the set of solutions of [*] has a basis of the form o,(z) = 2*p,(z), where

p, ...

Page 1527

To deal with the confluent hypergeometric

some of the theory of

Lj = (d/dz)”f+p(z)(d/dz)f-i-q(z)f = 0 to have an irregular singularity of order (or type)

...

To deal with the confluent hypergeometric

**equation**we must consequently usesome of the theory of

**equations**with ... It is most convenient to take the**equation**Lj = (d/dz)”f+p(z)(d/dz)f-i-q(z)f = 0 to have an irregular singularity of order (or type)

...

Page 1528

The first of these algebraic

of the differential

differential

irregular ...

The first of these algebraic

**equations**, which is simply the characteristic**equation**of the differential

**equation**, ... + o-1)2)}z-of, f being a solution of the originaldifferential

**equation**Lj = 0, we find that L'f' has rational coefficients, and anirregular ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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 Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity 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