## Linear Operators: Spectral theory |

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Page 1297

If Alf ) = 0 for each function in the domain of T ( T ) which vanishes in a neighborhood of a , A will be

If Alf ) = 0 for each function in the domain of T ( T ) which vanishes in a neighborhood of a , A will be

**called**a boundary value at a . The concept of a boundary value at b is defined similarly . By analogy with Definition XII.4.25 an ...Page 1432

In this case , v is

In this case , v is

**called**the order of the singularity of equation [ * ] at zero . If v = 0 , there is no singularity at all , and zero is**called**a regular point of the differential equation . If v = 1 , the singularity of equation ...Page 1451

The number c is

The number c is

**called**a bound for T , and the smallest ( largest ) such c is**called**the upper ( lower ) bound for T. If ( Tx , x ) 2 0 for all x in D ( T ) , then T is**called**nonnegative . 20 DEFINITION . Lett be a formally symmetric ...### 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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk 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