## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1050

We begin our formal development by considering a Lebesgue measurable

We begin our formal development by considering a Lebesgue measurable

**function**f**defined**on Euclidean n - space E , supposing that f has a finite number of singularities ” at which it is not Lebesgue integrable , and defining a certain ...Page 1074

10 Let be a

10 Let be a

**function defined**on ( -00 , +00 ) which is of finite total variation . Show that if i < p 2 , and if F is the Fourier transform of a function in L , ( - 00 , +00 ) , then so is 2 ( • ) F ( - ) . Fourier transforms are to be ...Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula defines an ... the self adjoint operator T and let f be a complex Borel

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula defines an ... the self adjoint operator T and let f be a complex Borel

**function defined**E - almost everywhere on the real axis .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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 function f 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 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 vanishes vector zero