## Linear Operators: Spectral theory |

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Page 1297

If A(f) = 0 for each function in the domain of Ti(r) 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(f) = 0, ...

If A(f) = 0 for each function in the domain of Ti(r) 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(f) = 0, ...

Page 1432

In this case, v is

there is no singularity at all, and zero is

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

singularity; ...

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 y = 1, the singularity of equation [*] at zero is

**called**a regularsingularity; ...

Page 1504

A point zo in the complex plane at which ri and r2 are analytic is

point of the operator. In the neighborhood of a regular point zo, there exists a

unique analytic solution f(z) of the equation Lj = 0 with specified initial values f(zo

), ...

A point zo in the complex plane at which ri and r2 are analytic is

**called**a regularpoint of the operator. In the neighborhood of a regular point zo, there exists a

unique analytic solution f(z) of the equation Lj = 0 with specified initial values f(zo

), ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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