## Linear Operators: Spectral theory |

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Page 1527

The same process applied to the hypergeometric

y ; z ) satisfies the confluent hypergeometric

dza dz This

The same process applied to the hypergeometric

**equation**[ 1 ] shows that Ø ( @ ,y ; z ) satisfies the confluent hypergeometric

**equation**[ 7 ] 2 ( ) + ( y - 2 ) 0 - 9 = 0 .dza dz This

**equation**has singularities at zero and infinity . The singularity at ...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**, is quadratic ... f being a solution of the originaldifferential

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

Page 1529

The confluent hypergeometric

, so that $ 11 ) = 0 , 5L = 1 . Thus the Stokes lines for this

and negative imaginary axes . Trying solutions of the form z - 1 ( 1 + ci2 + .

The confluent hypergeometric

**equation**has the characteristic**equation**a 2 - a = 0, so that $ 11 ) = 0 , 5L = 1 . Thus the Stokes lines for this

**equation**are the positiveand negative imaginary axes . Trying solutions of the form z - 1 ( 1 + ci2 + .

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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 |

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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