## Linear Operators, Part 2 |

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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 ; 2 ) satisfies the confluent hypergeometric**equation**d2 ( 2 ) d + ( y - 2 ) 0 - a0 0 . 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**... + $ ( k - 1 ) x ) } r - ef , f being a solution of the original differential**equation**Ls = 0 , we find that L'f ' has ...Page 1553

G3 Suppose that the operator t has the property that for some À the derivative of every square - integrable solution of the

G3 Suppose that the operator t has the property that for some À the derivative of every square - integrable solution of the

**equation**( 1-1 ) } = 0 is bounded . Prove that t has no boundary values at infinity .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

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 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 Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero