## 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**...Page 1504

A point zo in the complex plane at which r , and r , are analytic is

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

unique analytic solution f ( ) of the equation Lf = 0 with specified initial values f (

20 ) ...

A point zo in the complex plane at which r , and r , are analytic is

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

unique analytic solution f ( ) of the equation Lf = 0 with specified initial values f (

20 ) ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present 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 unit vanishes vector zero