## Linear Operators: Spectral operators |

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Page 2307

The last example above illustrates a problem which will be of great concern to us in the remainder of this chapter : the problem of finding which formal differential operators and sets of

The last example above illustrates a problem which will be of great concern to us in the remainder of this chapter : the problem of finding which formal differential operators and sets of

**boundary conditions**lead to spectral operators .Page 2344

interval [ 0 , 1 ] and by a set of n linearly independent

interval [ 0 , 1 ] and by a set of n linearly independent

**boundary conditions**, of which n / 2 are**boundary conditions**at zero and n / 2 are**boundary conditions**at 1. Then all the conclusions of Theorem 8 are valid .Page 2350

U - TU is the same as the operator in Hilbert space defined by the formal differential operator ( -id / dt + b ' ( t ) ) " and the set C / ( Uf ) = 0 , i = 1 ... n , of

U - TU is the same as the operator in Hilbert space defined by the formal differential operator ( -id / dt + b ' ( t ) ) " and the set C / ( Uf ) = 0 , i = 1 ... n , of

**boundary conditions**. Since 72 n ' din - 1 ( - :-) +61 ) + v ( m ) ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1931 |

Copyright | |

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero