## Linear Operators: Spectral theory |

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Page 1154

Since the product group R ( 2 ) = Rx R is locally compact and o - compact , it has

a Haar measure 2 ( 2 ) defined on its Borel field { ( 2 ) and what we shall prove is

that for some

Since the product group R ( 2 ) = Rx R is locally compact and o - compact , it has

a Haar measure 2 ( 2 ) defined on its Borel field { ( 2 ) and what we shall prove is

that for some

**constant**c , ( R ( 2 ) , 2 ( 2 ) , 2 ( 2 ) ) = c ( R , E , 2 ) * ( R , 2 , 2 ) .Page 1177

Subtracting a suitable

suppose without loss of generality that kn ... here we have used the uniform

boundedness of the functions k , and of their variations to conclude that the

Subtracting a suitable

**constant**cn from each of the functions kn , we maysuppose without loss of generality that kn ... here we have used the uniform

boundedness of the functions k , and of their variations to conclude that the

**constants**on are ...Page 1730

Moreover , there exists a

70 ( C ) . Now we shall prove an important lemma on elliptic partial differential

equations with

Moreover , there exists a

**constant**A < oo such that l ( tf , g ) | S All logo ) , f , g € 0 ,70 ( C ) . Now we shall prove an important lemma on elliptic partial differential

equations with

**constant**coefficients . 18 LEMMA . Let o be a formal partial ...### What people are saying - Write a review

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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 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