## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1527

The same process applied to the hypergeometric

The same process applied to the hypergeometric

**equation**[ 1 ] shows that ( a , y ; z ) satisfies the confluent hypergeometric**equation**d2 [ 7 ] d 0+ ( y - 2 ) φ– αφ = 0 . dz dz2 This**equation**has singularities at zero and infinity .Page 1528

The first of these algebraic

The first of these algebraic

**equations**, which is simply the characteristic**equation**of the differential**equation**... find the differential**equation**L'f ' = 0 satisfied by f ' = { exp ( 5 ( 1 ) k - 1 + + 51k - 1 ) ) } z- , f being a ...Page 1529

The confluent hypergeometric

The confluent hypergeometric

**equation**has the characteristic**equation**a ? - = 0 , so that $ ( 1 ) = 0,5 ) = 1. Thus the Stokes lines for this**equation**are the positive and negative imaginary axes . Trying solutions of the form z - 1 ( 1 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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 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 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