## 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 | |

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