## Linear Operators: Spectral theory |

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Page 1248

A bounded linear operator P in Hilbert space H is

is a closed subspace M such that \ Px | = | a | for x in M and P ( M - ) = { 0 } . The

subspace M is

A bounded linear operator P in Hilbert space H is

**called**a partial isometry if thereis a closed subspace M such that \ Px | = | a | for x in M and P ( M - ) = { 0 } . The

subspace M is

**called**the initial domain of P and PM ( = PH ) is**called**the final ...Page 1297

If Alf ) = 0 for each function in the domain of T ( 1 ) 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 ( 1 ) ...

If Alf ) = 0 for each function in the domain of T ( 1 ) 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 ( 1 ) ...

Page 1645

A very complete and interesting development of such a theory of generalized

functions was given by Laurent Schwartz ; the generalized functions were

by him " distributions . ” It is the purpose of the present section to develop those ...

A very complete and interesting development of such a theory of generalized

functions was given by Laurent Schwartz ; the generalized functions were

**called**by him " distributions . ” It is the purpose of the present section to develop those ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive 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 differential equations 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 neighborhood norm obtained partial positive preceding present problem Proc 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