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

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Page 1472

τσ least one such

τσ least one such

**solution**must exist . On the other hand , if two linearly independent**solutions**of to = lo satisfy the boundary condition B , it follows that all**solutions**of to = ho satisfy B. By the remark ( a ) made above , it then ...Page 1521

Putting yo = 1 / 2 + i so that ho = 1 + i , we see that the equation ( L - 2 ) has one

Putting yo = 1 / 2 + i so that ho = 1 + i , we see that the equation ( L - 2 ) has one

**solution**of the order of t - 1 - i as t = 0 and another which behaves like t ' as t → 00. The**solution**at ho = 1 - i is exactly similar .Page 1529

Then in this angle any

Then in this angle any

**solution**of L1 = 0 whose asymptotic expansion begins with the factor exp ( 511 ) k - 1 ) is exponentially small ( as 121 + 0 in the angle ) relative to any**solution**whose asymptotic expansion begins with the ...### 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