## Linear Operators: Spectral theory |

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Page 1297

If A ( t ) = 0 for each function in the domain of T ( T ) which vanishes in a

neighborhood of a , A will be

boundary value at b is defined similarly . By analogy with Definition XII . 4 . 25 an

equation B ...

If A ( t ) = 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 aboundary value at b is defined similarly . By analogy with Definition XII . 4 . 25 an

equation B ...

Page 1432

In this case , v is

, there is no singularity at all , and zero is

equation . If v = 1 , the singularity of equation [ * ] at zero 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 differentialequation . If v = 1 , the singularity of equation [ * ] at zero is

**called**a regular ...Page 1451

The number c is

the upper ( lower ) bound for T . If ( Tx , x ) 20 for all x in D ( T ) , then T is

nonnegative . 20 DEFINITION . Lett be a formally symmetric formal differential ...

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 ) 20 for all x in D ( T ) , then T is

**called**nonnegative . 20 DEFINITION . Lett be a formally symmetric formal differential ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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