## Linear Operators: Spectral theory |

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Page 1505

0 A regular point of a differential

regular singular point at which the exponents are zero and one . If Lf = 0 is a

differential

0 A regular point of a differential

**equation**may be regarded as a special case of aregular singular point at which the exponents are zero and one . If Lf = 0 is a

differential

**equation**with rational coefficients and a regular singularity z , with ...Page 1527

To deal with the confluent hypergeometric

some of the theory of

Lf ( d ) dz ) 21 + p ( z ) ( d / dz ) f + 9 ( z ) f = 0 to have an irregular singularity of ...

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**Lf ( d ) dz ) 21 + p ( z ) ( d / dz ) f + 9 ( z ) f = 0 to have an irregular singularity of ...

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 ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic 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 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 Nauk 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